Mechanisms of chromosome biorientation and bipolar spindle assembly analyzed by computational modeling

  1. Christopher Edelmaier
  2. Adam R Lamson
  3. Zachary R Gergely
  4. Saad Ansari
  5. Robert Blackwell
  6. J Richard McIntosh
  7. Matthew A Glaser
  8. Meredith D Betterton  Is a corresponding author
  1. Department of Physics, University of Colorado Boulder, United States
  2. Department of Molecular, Cellular, and Developmental Biology, University of Colorado Boulder, United States
8 figures, 8 videos, 8 tables and 3 additional files

Figures

Schematic of computational model and simulation of the reference model.

(A) Schematic of initial condition, showing adjacent spindle-pole bodies (blue) embedded in the nuclear envelope (gray dashed), proximal chromosomes (gray with green plate and blue springs), short microtubules (pink), and motor proteins and crosslinkers (red, blue, and black). (B) Schematic of bipolar spindle and a bioriented chromosome. (C) Schematic of chromosome and kinetochore model showing sister chromatids (gray), one kinetochore on each chromatid (green plates), the pericentric chromatin spring (blue springs), and kinetochore-MT attachment factor (blue line). (D) Schematic of chromosome attachment states, showing amphitelic, merotelic, monotelic, syntelic, and lost chromosomes. (E) Schematic of progressive restriction, showing that the angular range of kinetochore-MT attachment is restricted after attachment. (F) Schematic of misaligned destabilization of attachment, showing that misaligned attachments are destabilized. (G) Schematic of force stabilization of attachment, showing that end-on attachment to depolymerizing MTs has increased lifetime. (H) Image sequence of spindle assembly and chromosome biorientation rendered from a three-dimensional simulation. Initially, spindle-pole bodies (SPBs) are adjacent (blue disks), MTs are short spherocylinders (green and purple when unattached to kinetochores, yellow and magenta when attached), and chromosomes (cyan, yellow, magenta) are near SPBs. Motors and crosslinkers are dispersed spots (red, blue, and black) within the nucleus (gray boundary). Time shown in minutes:seconds. Lower: a zoomed view of each chromosome with attachment state labeled.

Figure 1—source data 1

Configuration files for the simulations used for snapshots in Figure 1H.

https://cdn.elifesciences.org/articles/48787/elife-48787-fig1-data1-v2.gz.zip
Figure 2 with 1 supplement
Comparison of spindle assembly and chromosome alignment in cells and simulations.

(A–D) Experimental results. (A) Maximum-intensity-projected smoothed images from time-lapse confocal fluorescence microscopy of fission yeast with mCherry-atb2 labeling MTs (red) and cen2-GFP labeling the centromere of chromosome 2 (green). Time shown in minutes:seconds. (B) Spindle length, (C) spindle pole body-kinetochore distance, and (D) interkinetochore distance versus time for the experiment shown in (A). (E–K) Simulation results. (E) Simulated fluorescence microscopy images with MTs (red) and a single kinetochore pair (green). (F) Spindle length, (G) spindle pole body-kinetochore distance, and (H) interkinetochore distance versus time from the simulation shown in (E), sampled at a rate comparable to the experimental data in (A–D). Note that the rigid nucleus in our model sets an upper limit on spindle length of 2.75 μm, as shown by the dashed line in F. (I) Spindle length versus time for 12 simulations of the reference model. (J) Spindle length versus time for 12 simulations in a model lacking kinesin-5. (K) Spindle length versus time for 12 simulations in a model lacking crosslink-mediated microtubule stabilization. (L) Fraction of simultaneous biorientation for the reference, kinesin-5 delete, and no-stabilization models (N = 12 simulations per data point).

Figure 2—source data 1

Configuration and data files for the simulations used in Figure 2.

Configuration files are contained within *config.tar.gz. Data are contained within *data.csv files.

https://cdn.elifesciences.org/articles/48787/elife-48787-fig2-data1-v2.gz.zip
Figure 2—figure supplement 1
Results of simulations with perturbations to motor and crosslinker number, motor force-dependent unbinding, and nuclear envelope rigidity.

(A) Simulated spindles form and biorient chromosomes in the absence of kinesin-14 motors if kinesin-5 and crosslinker number are increased. (B) Simulated spindles have difficulty forming in the absence of crosslinkers, and do not properly biorient chromosomes. (C) Lowering the characteristic distance of force-dependent unbinding of kinesin-14 to that of kinesin-5 (which makes kinesin-14 motors less sensitive to force-induced unbinding) causes longer spindles to form that are capable of biorienting chromosomes. (D) Spindle length as a function of wall force for a model of a soft nuclear envelope for which the SPBs are not fixed on the surface of the sphere. The reference model contains 174 kinesin-5 motors, 230 kinesin-14 motors, and 657 crosslinkers. (N = 12 simulations per data point.).

Figure 2—figure supplement 1—source data 1

Configuration and data files for simulations used in Figure 2—figure supplement 1.

Configuration files are contained within the *config.tar.gz files. Data are contained within the MATLAB scripts *panelA-D.m.

https://cdn.elifesciences.org/articles/48787/elife-48787-fig2-figsupp1-data1-v2.gz.zip
Figure 3 with 1 supplement
Results of perturbing kinetochore properties required for biorientation.

(A) Fraction simultaneous biorientation versus angular spring stiffness in models lacking progressive restriction of attachment. (B) Fraction simultaneous biorientation versus the first angular spring stiffness in the model with progressive restriction. (C) Fraction simultaneous biorientation versus the third angular spring stiffness in the model with progressive restriction. (D) Fraction simultaneous biorientation versus the misaligned destabilization factor. (E) Effects of force-dependent error correction. Top, schematic of stabilization of kinetochore-MT attachments as a function of interkinetochore force. Left, Stabilization as a function of interkinetochore tension for a characteristic force of 1.67 pN. When the interkinetochore force is the characteristic force, attachment turnover is reduced by a factor of two, as shown by the red dashed lines. Right, fraction simultaneous biorientation versus the characteristic force. (F) Fraction simultaneous biorientation for different types of force-dependent kinetics (N = 12 simulations per data point).

Figure 3—source data 1

Configuration and data files for simulations used in Figure 3.

Configuration files are contained within *config.tar.gz. Data are contained within *data.csv files, except for Figure 3E, where the data are contained within the python script Figure 3e_graphcreation.py.

https://cdn.elifesciences.org/articles/48787/elife-48787-fig3-data1-v2.gz.zip
Figure 3—figure supplement 1
Effects of varying the middle angular stiffness for progressive restriction and the number of kinetochore-microtubule attachments.

(A) Angular spring stiffness for the middle value chosen in progressive restriction did not affect chromosome biorientation fidelity. In these models, the first and third angular spring stiffnesses were fixed at 1 kBT and 100 kBT, respectively. (B) Varying the number of microtubule attachment sites per kinetochore does not significantly alter biorientation in the model. We varied the angular spring stiffnesses are varied with the number of attachments shown as (1: [1 kBT, 1 kBT], 2: [1 kBT, 10 kBT, 10 kBT], 3: Reference model, 4–6: [1 kBT, 10 kBT, 100 kBT, 100 kBT, … 100 kBT]) (N = 12 simulations per data point).

Figure 3—figure supplement 1—source data 1

Configuration and data files for simulations used in Figure 3—figure supplement 1.

Configuration files are contained within the *config.tar.gz files. Data are contained within the *data.csv files.

https://cdn.elifesciences.org/articles/48787/elife-48787-fig3-figsupp1-data1-v2.gz.zip
Changes in kinetochore-MT attachment turnover alter spindle length fluctuations.

(A–C) Spindle length versus time for 24 simulations of the same model, with (A) short (1/4 the reference value), (B) intermediate (1/2 the reference value), and (C) long (twice the reference value) kinetochore-MT attachment lifetime. (D) Length fluctuation magnitude versus measured kinetochore-MT attachment lifetime and average interkinetochore stretch (color) for bioplar spindles (corresponding to simulation time >10 min.). (E) Length fluctuation magnitude versus measured kinetochore-MT attachment lifetime and average interkinetochore stretch (color) for the reference, restricted, and weak rescue models (N = 24 simulations per data point).

Figure 4—source data 1

Configuration and data files for simulations used in Figure 4.

Configuration files are contained within *config.tar.gz files for the noted panels. Figure 4A–C data contained within *data.csv files that pertains to the spindle length versus time measurements. Data for panels Figure 4D,E are contained in their respective files as well, but contain data for the kinetochore-microtubule attachment lifetimes and length fluctuations measurements.

https://cdn.elifesciences.org/articles/48787/elife-48787-fig4-data1-v2.gz.zip
Spindle force generation varies as the spindle assembles and elongates.

(A) Schematic of force generation along the spindle axis, showing kinesin-5 motors exerting outward force (red) and kinesin-14 (dark blue), crosslinkers (black), and kinetochore-MT attachment to stretched chromosomes (light blue) exerting inward force. (B, E, H) Spindle length versus time, (C, F, I) average spindle axis force versus time, and (D, G, J) average spindle axis force versus spindle length for three different models: (B–D) the reference model, (E–G) the restricted attachment model, and (H–J) the weak rescue model (N = 24 simulations per data point).

Figure 5—source data 1

Configuration and data files for simulations used in Figure 5.

Configuration files are contained within *config.tar.gz files for the noted panels. Spindle length versus time measurements are found within Figure 5b,e,h_data.csv files. Spindle force measurements are found within Figure 5cd,fg,ij_data.csv files.

https://cdn.elifesciences.org/articles/48787/elife-48787-fig5-data1-v2.gz.zip
Chromosome segregation in the model and comparison to experiments.

(A) Image sequence of simulation of chromosome segregation after anaphase is triggered, rendered from a three-dimensional simulation. Anaphase begins immediately after the first image. Lower, schematic showing kinetochore position along the spindle. Time shown in minutes:seconds. (B–D) Simulation results. (B) Simulated fluorescence microscopy images with MTs (red) and a single kinetochore pair (green). Time shown in minutes:seconds. (C) Spindle pole body-kinetochore distance, and (D) interkinetochore distance versus time from the simulation shown in (B), sampled at a rate comparable to the experimental data in (E–G). (E–G) Experimental results. Maximum-intensity projected smoothed images from time-lapse confocal fluorescence microscopy of fission yeast with mCherry-atb2 labeling MTs (red) and cen2-GFP labeling the centromere of chromosome 2 (green). Time shown in minutes:seconds. (E) Spindle length, (F) spindle pole body-kinetochore distance, and (G) interkinetochore distance versus time from the experiment shown in (E).

Figure 6—source data 1

Configuration and data files for simulations used in Figure 6.

Configuration files are contained within *config.tar.gz files for the noted panels. Spindle length data are found within the *data.csv files.

https://cdn.elifesciences.org/articles/48787/elife-48787-fig6-data1-v2.gz.zip
Appendix 1—figure 1
Chromosome model overview.

(A) Chromosomes are modeled as sister chromatids and kinetochores held together by a cohesin/chromatin spring complex. Each kinetochore can attach up to three microtubules. (B) Steric interactions between MTs and kinetochores prevent overlap, while a soft steric repulsion exists between MTs and the centromeric DNA. (C) Kinetochores are kept back-to-back through a cohesin-chromatin spring complex that depends on relative kinetochore position and orientation. (D) The angular range of kinetochore-MT attachment is restricted based on the stiffness of an angular spring. (E) The angular restriction of kinetochore-MT attachment changes based on the number of bound MTs. (F) Attachments are destabilized when the chromosome is not properly bioriented. (G) Attachment lifetime is force-dependent, with attachments to depolymerizing MTs under tension having longer lifetimes, while those to polymerizing MTs have their lifetime decreased under tension. (H) MT dynamics are force-dependent. Polymerizing MTs have increased growth speed and reduced catastrophe, while depolymerizing MTs have increased rescue and decreased shrinking speed.

Appendix 1—figure 2
Reference model generates similar dynamics of spindle length and kinetochore position compared to experiment.

(A) Spindle length versus time for experiment (blue) and refined model (red). (B) Spindle pole body-kinetochore distance versus time for a single kinetochore pair (Cen2) in experiment (blue, cyan) and refined model (red, magenta). (C) Kinetochore separation versus time for experiment (blue) and refined model (red). This comparison gives Pearson correlation coefficients for length = 0.891, SPB-KC distance = 0.72, Interkinetochore distance = 0.42.

Videos

Video 1
Simulation of the reference model shows spindle assembly simultaneous with chromosome biorientation.

Initially, short MTs begin to grow at the start of the simulation and interact with nearby kinetochores. A bipolar spindle forms as the chromosomes begin to biorient. Finally, a metaphase spindle is established with bioriented chromosomes that move along the spindle and breathe. The insets are zoomed views of each chromosome, showing attachment turnover and interkinetochore stretch.

Video 2
Top: Simulation of reference model (left) and simulated fluorescence microscopy images (right), with red MTs and green kinetochore (scale bar 1 μm).

The simulated fluorescence images are rotated so that the spindle is vertical. Lower: simulation of models mimicking genetic perturbation. Lower left: Model lacking kinesin-5 motors. The SPBs never separate and the spindle remains monopolar. Chromosomes do not biorient. Lower right: Model lacking crosslinker-mediated stabilization of MT dynamics. SPBs separate only slightly, forming a short spindle that is nearly indistinguishable from a monopolar spindle. Chromosomes do not biorient.

Video 3
Simulation of a model with a soft nuclear envelope and an asymptotic wall force on the SPBs of 17 pN.

SPBs are able to move away from their preferred radius from the center of the nucleus. The spindle reaches a bounded length, and chromosomes are able to biorient. Spindle length larger than the nuclear envelope radius is reached by the balance of force from motors, crosslinkers, chromosomes.

Video 4
Simulations of models with perturbation to kinetochore properties important for biorientation.

Top left: Model lacking progressive restriction, with a common angular spring stiffnesses of 1 kBT for all attachments. A short bipolar spindle forms, but chromosomes are typically merotelically attached and do not biorient. Top middle: Model lacking progressive restriction, with a common angular spring stiffnesses of 100 kBT for all attachments. A long bipolar spindle forms, kinetochore-MT attachments are transient, and chromosomes do not generate significant inward force on the spindle. Top right: Model including progressive restriction with an angular spring stiffness of 20 kBT for the first binding event, leading to restricted attachments. A long bipolar spindle forms, and kinetochore-MT attachments are transient. Lower left: model including progressive restriction but with an angular spring stiffness of 20 kBT for the third binding event, leading to permissive attachments. Error correction is impaired, and chromosomes are typically merotelically attached. Lower middle: Model lacking misaligned destabilization. Error correction is impaired. Lower right: Model with force-independent attachment kinetics. Kinetochore-MT attachments are not stabilized under tension from depolymerizing microtubules, leading to short-lived biorientation.

Video 5
Simulation of a model with interkinetochore force-dependent attachments.

The spindle forms in a few minutes, and chromosomes form stable, bioriented attachments. Zoomed views of chromosomes shows them forming load-bearing attachments to the tips of MTs. The interkinetochore characteristic force is 1.67 pN.

Video 6
Simulations of models with varying kinetochore-MT attachment lifetime.

Left: Model with short attachment lifetime in which the kinetochore-MT binding and unbinding rates are 4 times larger than in the reference model. Biorientation is somewhat compromised. Middle: Model with intermediate attachment lifetime in which the kinetochore-MT binding and unbinding rates are 2 times larger than in the reference model. Right: Model with long attachment lifetime in which the kinetochore-MT binding and unbinding rates are 2 times smaller than in the reference model. Biorientation is preserved and the spindle undergoes large length fluctuations.

Video 7
Simulations of reference, restricted, and weak rescue models.

Left: The reference model shows typical spindle length fluctuations. Middle: The restricted attachment model shows minimal length fluctuations, because transient kinetochore-MT attachments lead to low inward force on the spindle from chromosomes. Right: The weak rescue model shows large spindle length fluctuations, because kinetochore MTs remain attached while depolymerizing, leading to high and fluctuating inward force on the spindle from chromosomes.

Video 8
Simulations of anaphase chromosome segregation.

Top: Simulation video showing that separation of the sister chromatids occurs after 4.45 min of the simultaneous biorientation of all three chromosomes. The zoomed views show the chromosomes achieving biorientation before segregating to the spindle poles. Lower: Simulation video (left) and simulated fluorescence microscopy images (right), with red MTs and green kinetochore (scale bar 1 μm). The simulated fluorescence images are rotated so that the spindle is vertical. Anaphase occurs at 7:09.

Tables

Table 1
Simulation, SPB, and MT parameters.
Simulation parameterSymbolValueNotes
Time stepδt8.9 ×10-6 sBlackwell et al., 2017a
Nuclear envelope radiusR1.375 μmKalinina et al., 2013
Spindle pole bodies
DiameterσSPB0.1625 μmDing et al., 1993
Bridge size75 nmDing et al., 1993
Tether lengthR050 nmFlory et al., 2002; Muller et al., 2005
Tether spring constantK00.6625 pN nm-1Blackwell et al., 2017a
Translational diffusion coefficientDt4.5 × 10-4 μm2 s-1Blackwell et al., 2017a
Rotational diffusion coefficientDθ,spb0.0170 s-1Blackwell et al., 2017a
Linkage timeτlink5 sBlackwell et al., 2017a
Microtubules
DiameterσMT25 nmBlackwell et al., 2017a
Angular diffusion coefficientDθDepends on MT lengthBlackwell et al., 2017a; Kalinina et al., 2013
Force-induced catastrophe constantαc0.5 pN-1Blackwell et al., 2017a; Janson et al., 2003; Dogterom and Yurke, 1997
Growth speedvp,04.1 μm min-1Blackwell et al., 2017a; Blackwell et al., 2017b
Shrinking speedvs,06.7 μm min-1Blackwell et al., 2017a; Blackwell et al., 2017b
Catastrophe frequencyfc,03.994 min-1Blackwell et al., 2017a; Blackwell et al., 2017b
Rescue frequencyfr,00.157 min-1Blackwell et al., 2017a; Blackwell et al., 2017b
Growth speed stabilizationsvg1.54Optimized
Shrinking speed stabilizationsvs0.094Optimized
Catastrophe frequency stabilizationsfc0.098Optimized
Rescue frequency stabilizationsfr18Optimized
Stabilization lengths16 nmOptimized
Minimum MT lengthLmin75 nmOptimized
Table 2
Soft nuclear envelope model parameters.
ParameterSymbolValueNotes
Translational mobilityμSPBtb(0.050000.110000.11)μms1pN1Calculated
Rotational mobilityμSPBrb(16.60000.1660000.166)μm1s1pN1Calculated
Membrane tube radiusftube87.7 nmDerényi et al., 2002; Lim et al., 2007; Lamson et al., 2019
MT asymptotic wall forcefMT,w2.5 pNDerényi et al., 2002; Lim et al., 2007; Lamson et al., 2019
SPB asymptotic wall forcefSPB,w17 pNDerényi et al., 2002; Lim et al., 2007; Lamson et al., 2019
Tether spring constantK06.625 pN nm-1Optimized
Table 3
Motor and crosslinker parameters.
Simulation parameterSymbolValueNotes
Kinesin-5
NumberNK5174Optimized (Carpy et al., 2014)
Association constant per siteKa90.9 μM-1 site-1Cochran et al., 2004
One-dimensional effective concentrationc20.4 nm-1Blackwell et al., 2017a
Spring constantK0.3pNnm-1Kawaguchi and Ishiwata, 2001
Singly-bound velocityv0-100nms-1Roostalu et al., 2011
Polar aligned velocityv0,P-50nms-1Gerson-Gurwitz et al., 2011
Anti-polar aligned velocityv0,AP8nms-1Gerson-Gurwitz et al., 2011
Singly bound off-ratek10.11 s-1Roostalu et al., 2011
Doubly bound off-rate (single head)k20.055 s-1Blackwell et al., 2017a
Tether lengthR053 nmKashlna et al., 1996
Stall forceFs5 pNValentine et al., 2006
Characteristic distancexc1.5 nmOptimized (Arpağ et al., 2014
Diffusion constant (solution)Dfree4.5 μm2s-1Bancaud et al., 2009
Kinesin-14
NumberNK14230Optimized (Carpy et al., 2014)
Association constant (motor head)Ka,m22.727 μM-1 site-1Chen et al., 2012
Association constant (passive head)Ka,d22.727 μM-1 site-1Blackwell et al., 2017a
1D effective concentration (motor head)c2m0.1 nm-1Blackwell et al., 2017a
1D effective concentration (passive head)c2d0.1 nm-1Blackwell et al., 2017a
Spring constantK0.3pNnm-1Kawaguchi and Ishiwata, 2001
Singly bound velocity (motor head)v0m-50nms-1Blackwell et al., 2017a
Diffusion constant (bound, diffusing head)Dd0.1 μm2 s-1Blackwell et al., 2017a
Singly bound off-rate (motor head)k1m0.11 s-1Blackwell et al., 2017a
Singly bound off-rate (passive head)k1d0.1 s-1Blackwell et al., 2017a
Doubly bound off-rate (motor head)k2m0.055 s-1Blackwell et al., 2017a
Doubly bound off-rate (passive head)k2d0.05 s-1Blackwell et al., 2017a
Tether lengthR053 nmBlackwell et al., 2017a
Stall forceFs5.0 pNBlackwell et al., 2017a
Characteristic distancexc4.8 nmOptimized (Arpağ et al., 2014)
Adjusted characteristic distancexc1.5 nmFigure 2—figure supplement 1C
Crosslinker
NumberNXL657Optimized (Carpy et al., 2014)
Association constantKa90.9 μM-1 site-1Cochran et al., 2004
One-dimensional effective concentrationc20.4 nm-1Lansky et al., 2015
Spring constantK0.207 pN nm-1Lansky et al., 2015
Diffusion constant (solution)Dfree4.5 μm2s-1Bancaud et al., 2009
Singly bound diffusion constantDsb0.1 μm2 s1Lansky et al., 2015
Doubly bound diffusion constantDdb6.7×103μm2 s1Lansky et al., 2015
Singly bound off-ratek10.1 s-1Kapitein et al., 2008
Doubly bound off-ratek20.05 s-1Lansky et al., 2015
Parallel-to-antiparallel bindng ratioPaff0.33Kapitein et al., 2008; Rincon et al., 2017; Lamson et al., 2019
Characteristic distancexc2.1 nmOptimized (Arpağ et al., 2014)
Tether lengthR053 nmLansky et al., 2015; Lamson et al., 2019
Table 4
Chromosome and kinetochore parameters.
Simulation parameterSymbolValueNotes
Kinetochore kinematics
DiameterσKC200 nmBlackwell et al., 2017a; Kalinina et al., 2013
LengthLKC,0150 nmDing et al., 1993
WidthLKC,150 nmDing et al., 1993
ThicknessdKC0 nmChosen
Diffusion coefficientDKC5.9 × 10-4µm2 s-1Gergely et al., 2016; Blackwell et al., 2017a; Kalinina et al., 2013
Translational dragγKC,t3.51 pN µm-1 sComputed
Rotational dragγKC,r0.165 pN µm sComputed
Catastrophe enhancementsKC-cen,fc0.5 pN-1Matches NE factor
MT tip lengthlcen,tip25 nmChosen
Interkinetochore spring
Tether lengthRC,0100 nmStephens et al., 2013; Gergely et al., 2016; Gay et al., 2012
Linear spring constantκC39 pN µm-1Optimized
Rotational spring constantκC,u1850 pN nm rad-1Optimized
Alignment spring constantκC,v1850 pN nm rad-1Optimized
Pericentric chromatin
Pericentric chromatin lengthrcentromere200 nmChosen
Pericentric chromatin diameterdcentromere75 nmChosen
Kinetochore-centromere offsetrKC-cen37.5 nmChosen
Chromatin-MT repulsion amplitudeACMT1 pN nmOptimized
Table 5
Attachment factor parameters.
ParameterSymbolValueNotes
NumberNAF3Ding et al., 1993
Attachment-site separation on kinetochorerAF,ex40 nmDing et al., 1993
Linear spring constantκAF,m0.088 pN nm-1Optimized
Angular spring constant, 0 to 1κAF,r,04.1 pN nmOptimized
Angular spring constant, 1 to 2κAF,r,141 pN nmOptimized
Angular spring constant, 2 to 3κAF,r,2410 pN nmOptimized
Angular spring constant, 3 to 3κAF,r,3410 pN nmOptimized
Tether lengthrAF,054 nmCiferri et al., 2007
kMC stepsNkmc10Chosen
MT tip lengthlAF,tip25 nmChosen
MT tip crowdingbAF,tipTrueDing et al., 1993
Tip concentrationcAF,tip40 nm-1Optimized
Side concentrationcAF,side0.4 nm-1Optimized
Tip rate assemblingkAF,tip,a0.0001 s-1Optimized
Tip rate disassemblingkAF,tip,d0.03 s-1Optimized
Side ratekAF,side0.03 s-1Optimized
Tip characteristic distance assemblingxc,t,a1 nmOptimized
Tip characteristic distance disassemblingxc,t,d−3.9 nmOptimized
Side characteristic distancexc,s−0.37 nmOptimized
Angular characteristic factorχc0.013Optimized
SpeedvAF50 nm s-1Optimized
Stall forcefAF,stall5 pNKinesin-5 (Blackwell et al., 2017a; Akera et al., 2015)
Tip diffusionDtip0.0012 μm2 s-1Optimized
Side diffusionDside0.018 μm2 s-1Optimized
Tip trackingfAF,track0.25Optimized
Tip-enhanced catastrophesfc,dam14Optimized
Misaligned destabilizationsk,ABK70Optimized
Polymerization force factorFAF,vg8.4 pNAkiyoshi et al., 2010; Gergely et al., 2016
Depolymerization force factorFAF,vs−3.0 pNAkiyoshi et al., 2010; Gergely et al., 2016
Catastrophe force factorFAF,fc−2.3 pNAkiyoshi et al., 2010; Gergely et al., 2016
Rescue force factorFAF,fr6.4 pNAkiyoshi et al., 2010; Gergely et al., 2016
Maximum polymerization speedvAF,MT,max30 μm min-1Gergely et al., 2016
Table 6
Force-dependent error correction model parameters.
ParameterSymbolValueNotes
Inter-kinetochore stabilization forceFEC,01.67 pNOptimized
Rotational spring constantκC,u925 pN nm rad-1Optimized
Alignment spring constantκC,v925 pN nm rad-1Optimized
Angular characteristic factorχc0.08Optimized
Side concentrationcAF,side0.32 nm-1Optimized
Kinesin-5 numberNK5200Optimized
Table 7
Anaphase parameters.
AnaphaseSymbolValueNotes
Integrated simultaneous biorientation timeτSAC4.45 minChosen
Anaphase attachment ratekAF,anaphase0.00007 s-1Chosen
Anaphase MT depoly speedvanaphase,s,02.2 µm min-1Chosen
Appendix 1—table 1
Strain used in this study.
NameGenotypeNotes
MB 998cen2::kanr-ura4+-lacOp, his7+::lacI-GFP, z:adh15:mCherry-atb2:natMX6, leu1-32, h-This study

Additional files

Source code 1

Code for simulation and analysis framework for confined SPB simulations.

Requires C++ compiler, and GSL, GLEW, python2, python3, libyaml, FFTW, GLFW, xQuartz, freeGLUT, libpng, ffmpeg, pkg-config, and png++ libraries. Python libraries should include matplotlib, numpy, opencv-python, panda3d, pandas, PyYAML, and scipy for analysis framework. Used for all simulations except Figure 2—figure supplement 1, panel D: Soft nuclear envelope. Untar and unzip SourceCodeFile1.tar.gz, then use the accompanying Makefile and MakefileIncmk to compile on your system.

https://cdn.elifesciences.org/articles/48787/elife-48787-code1-v2.tar.gz
Source code 2

Code for simulation and analysis framework for free SPB simulations.

Requires C++ compiler, and armadillo, GSL, GLEW, python2, python3, libyaml, FFTW, GLFW, xQuartz, freeGLUT, libpng, ffmpeg, pkg-config, and png++ libraries. Python libraries should include matplotlib, numpy, opencv-python, panda3d, pandas, PyYAML, and scipy for analysis framework. Used only for Figure 2—figure supplement 1, panel D: Soft nuclear envelope. Untar and unzip SourceCodeFile2.tar.gz, then use the accompanying Makefile and MakefileIncmk to compile on your system.

https://cdn.elifesciences.org/articles/48787/elife-48787-code2-v2.tar.gz
Transparent reporting form
https://cdn.elifesciences.org/articles/48787/elife-48787-transrepform-v2.docx

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  1. Christopher Edelmaier
  2. Adam R Lamson
  3. Zachary R Gergely
  4. Saad Ansari
  5. Robert Blackwell
  6. J Richard McIntosh
  7. Matthew A Glaser
  8. Meredith D Betterton
(2020)
Mechanisms of chromosome biorientation and bipolar spindle assembly analyzed by computational modeling
eLife 9:e48787.
https://doi.org/10.7554/eLife.48787