Stochastic force-balance model for antagonistic motility assays incorporating KLP61F and Ncd kinetics: model fit to assay data identifies motors’ biophysical parameters and suggests load-dependent kinetics and a specific superstall F–V relationship for motors. (A) Experimental (black) and computed (red) MT velocities in competitive gliding assays. The mole fraction is defined as (mole Ncd)/(mole Ncd + mole KLP61F), ignoring solvent/buffer concentrations. The stochastic force-balance model provides an excellent fit to the mean and the SD of the gliding data, even at the balance point. (B) Histogram of experimental (black) and computed (red) MT velocities at the balance point mole fraction with respective Gaussian fits. (C) Computed trajectories of four representative MTs at the balance point. (D) Histogram of the number of KLP61F and Ncd motors engaged with an MT (computed). Asterisks indicate peaks.

Gliding assays with purified Ncd and HL-KLP61F or KLP61F stalk: stochastic force-balance model that includes motors’ kinetics accounts for the results, but a protein friction model does not. (A) Competitive gliding assay results for Ncd with HL-KLP61F (left) and KLP61F stalk (right) for various mole fractions of Ncd, ranging from 0 to 1. (B) Results of stochastic, opposing power stroke force-balance model (red) including the kinetics of individual motors superimposed on experimental results (black). (A and B) Error bars show SD. (C) Histogram of distances MTs travel at the balance point mole fraction (∼0.7; in gliding assays shown in A) and the Gaussian distribution fit (red).

Functional perturbation of the lamin-B envelope interferes with spindle length changes and the completion of mitosis. (A) Microinjection of the lamin-B tail dominant-negative (DN) subfragment disrupts the lamin-B nuclear lamina and causes delays in prometaphase spindle formation, destabilization and length fluctuations of the phase I spindles, defects in subsequent spindle morphogenesis, and failure to complete mitosis. (B) The microinjection of a mixture of anti–lamin-B mAbs cross-links the lamin-B envelope into a hyperstable network that fails to disassemble. This structure impedes spindle elongation during prometaphase phase II and anaphase B (graph; arrows show times when still images were captured). In A and B, panels show still images at times after NEB. In A, t = 0 corresponds to NEB for spindle s1. Top and bottom graphs show pole–pole spacing versus time after NEB (t = 0) for multiple spindles (mean with SD) and individual spindles (A, second row: the left graph shows multiple control spindles [black]; for clarity, the right graph shows a single control spindle [black]). Bars, 10 μm.

Prometaphase spindle dynamics in Drosophila embryos: steady-state and elongation phases. (A, top) Time series of a spindle in living transgenic Drosophila embryos expressing GFP-tubulin (green) and histone-RFP (red) taken at the indicated time points on the plot of pole–pole spacing from the same spindle (red arrows on inset of bottom panel; t = 0 is NEB). (bottom) Averaged and normalized pole–pole dynamics in cycle 11 Drosophila embryo spindles; t = 0 is NEB. Prometaphase dynamics (blue): the steady-state (I) and elongation (II) phases are shown. Error bars show SD. (B) The top two rows show KLP61F-GFP (first row) and Ncd-GFP (second row) localization during prometaphase (phase I; steady-state) in restored spindles (deconvolved 3D image stacks), respectively. The left panels are 3D views of restored spindles, and the right panels show a single z plane from the same spindles. The bottom two rows show the colocalization of KLP61F-GFP and Ncd-GFP with rhodamine-tubulin on the nascent ipMTs during prometaphase (phase I; steady-state). (C, top) Averaged and normalized prometaphase pole–pole dynamics from cycle 11 embryos in wild type, control IgG, Ncd null, and KLP61F antibody–injected wild-type (black) and Ncd null (red). Error bars show SD. (middle) Data from the top panel are shown without SDs for clarity. (bottom) Pole–pole dynamics in individual representative spindles. (D) Cartoon of phase I (left) and II (right) prometaphase spindles based on in vivo functional perturbation and localization data. Colored arrows below the drawings indicate the direction of the forces generated by corresponding motors. Bars, 5 μm.

A lamin-B envelope confers robustness to the steady-state prometaphase spindle by stabilizing it to phenotypic variations in the KLP61F to Ncd ratio. (A) Localization of the Drosophila lamin-B (Dm0) surrounding the prometaphase (phase I and II) spindle in fly embryos stably expressing GFP-Dm0; t = 0 is NEB. Images show a time series from a live embryo, each image being a projection of six z stacks along the x–y plane. Note the indentation of the lamin-B envelope surrounding the spindle by the centrosomes at the opposite ends of the spindle at t = 36 and 72 s during prometaphase phase I. (B) Schematic representation of an elastic lamin-B envelope surrounding the spindle during phase I of prometaphase and the representation of this envelope as a linear Hookean spring between the spindle poles (simple drawings above the spindle cartoons). Green and red arrows depict KLP61F- and Ncd-driven ipMT sliding. The time-dependent disassembly of this elastic envelope is incorporated into the quantitative model as a linearly decreasing spring constant, ζ(t), responding equally to extension and compression as shown in the graph on the right (solid line). Superimposed is an asymmetric spring constant of the lamin-B envelope with limited compressibility (dashed line). (C) Quantitative model results of the role of the elastic lamin-B envelope on the robustness of the prometaphase steady-state to the motors’ molar ratio. The left panel shows the mean prometaphase spindle length over time (averaged over 10 virtual spindles) for the varying mole fraction of Ncd, increasing from 0 to 1 in 31 equally spaced steps. The right panel shows the mean pole–pole separation rate for increasing Ncd mole fraction from 0 to 1; results of the model augmented with an elastic lamin-B envelope (red) are superimposed on the model solutions without lamin-B (black), as in Fig. 4 D, for comparison. A stable spindle length (mean velocity ≤|0.02| μm s⁻¹) is maintained for a wide range of motors’ molar ratio (approximately within [0.35 to 0.8] Ncd mole fraction) in the solution of the augmented model (red). The solution of the model including a lamin-B envelope with asymmetric response to extension and compression as in B (right, dashed line) is shown superimposed in blue. This extends the stability regime further, particularly at high Ncd mole fractions. Error bars show SD. Bar, 5 μm.

Quantitative stochastic force-balance model of the prometaphase phase I spindle: spindle MT and motor properties reveal a finely tuned steady-state. (A, from left to right) Spindle length, total AP overlap, and number of engaged Ncd and KLP61F motors on the AP overlaps during Phase I. Mole fraction of available Ncd is 0.7 (i.e., ∼2 Ncd per KLP61F). (B, top) Experimental (left) and computed (right) tubulin kymograph starting at NEB (t = 0) during prometaphase. (bottom) The corresponding pole–pole (PP) dynamics, experimental (black) and computed (blue), are shown. (C) Computed normalized spindle length dynamics in representative individual spindles: wild type (blue), Ncd null (orange), and KLP61F antibody injected into wild-type (black) or Ncd-null background (red). (D, left) Mean prometaphase phase I spindle dynamics for varying mole fractions of Ncd, increasing from 0 to 1 in 31 equally spaced steps. At t = 0 (NEB) MTs (not depicted) begin invading the spindle region. (right) Mean pole–pole separation rate (mean of instantaneous velocities during the last 40 s of prometaphase in 10 virtual spindles) plotted for varying Ncd mole fractions. The steady-state separation (mean velocity is ∼0) is confined to a narrow range of Ncd mole fractions. Error bars show SD. (E) Measurement of the molar ratio of endogenous KLP61F to Ncd. (left) Western blots showing (a) polypeptides from a serial dilution of recombinant protein (standard) purified from baculovirus expression system on the left and (b) corresponding polypeptides in high speed supernatants (HSS) from Drosophila embryo lysates; KLP61F was detected by anti-KLP61F antibody (top), and Ncd was detected by anti-Ncd antibody (bottom). (right) Corresponding standard curves showing polypeptide density versus standard protein’s amount from the left panels (KLP61F standards are shown as black dots, and Ncd standards are shown as gray dots). The amount of standard protein loaded was adjusted so that the densities of the endogenous protein (labeled as high speed supernatant; two different loading volumes for each protein) fell within the linear range, i.e., the middle of the standard curve. The amount of endogenous KLP61F and Ncd were calculated from linear fits to the standard curves. AU, arbitrary unit.