DOI: 10.5061/dryad.xksn02vnb
title: Paired microtubules growing with a shared load

description: During mitosis, kinetochore-attached microtubules form bundles (k-fibers)
 in which many filaments grow and shorten in near-perfect unison to align
 and segregate each chromosome. However, individual microtubules grow at
 intrinsically variable rates, which must be tightly regulated for a
 k-fiber to behave as a single unit. This exquisite coordination might be
 achieved biochemically, via selective binding of polymerases and
 depolymerases, or mechanically, because k-fiber microtubules are coupled
 through a shared load that influences their growth. Here, we use a novel
 dual laser trap assay to show that microtubule pairs growing in vitro are
 coordinated by mechanical coupling. Kinetic analyses show that microtubule
 growth is interrupted by stochastic, force-dependent pauses and indicate
 persistent heterogeneity in growth speed during non-pauses. A simple model
 incorporating both force-dependent pausing and persistent growth speed
 heterogeneity explains the measured coordination of microtubule pairs
 without any free fit parameters. Our findings illustrate how microtubule
 growth may be synchronized during mitosis and provide a basis for modeling
 k-fiber bundles with three or more microtubules, as found in many
 eukaryotes.
description: The data here was collected using the 'dual-trap
 assay,' which is based on our previously developed single-trap
 (force-clamp) assay (Akiyoshi et al., 2010; Miller et al., 2016; Sarangapani et al., 2013), in which dynamic microtubules are grown from stabilized seeds bound to a biotinylated coverslip. Using the single laser trap, we attach an individual bead decorated with isolated yeast kinetochores to the growing plus-end of a single microtubule. A computer then continuously measures the bead position and adjusts the trap to exert a precise, constant level of tension on the microtubule via the kinetochore-decorated bead. Under this persistent feedback-controlled tension, kinetochore-beads typically track with the microtubule tips even as the tips stochastically grow and shorten. Our new dual-trap assay uses two separate laser trapping microscopes, located adjacent to one another in the same room and connected to a single computer. On each of the two instruments, we attach a kinetochore-decorated bead to a dynamic microtubule plus-end. The computer then simultaneously monitors and controls the forces on both microtubules. Rather than keeping the force constant on each microtubule, the computer adjusts the forces dynamically to simulate an elastic coupling of both plus-ends to a single shared load. Thus far, we have simulated only purely elastic couplers, where both coupling springs are linear (Hookean) with stiffness, <em>κ</em>. To begin a dual-trap experiment, we first choose the spring stiffness, <em>κ</em>, and the total shared load, <em>F<sub>TOT</sub></em>, which are kept constant. After a kinetochore-decorated bead is attached to a growing plus-end on each of the two instruments, feedback-control is initiated and the two plus-ends are arbitrarily considered to be parallel, with tips side-by-side (i.e., both at <em>x<sub>1</sub></em> = <em>x<sub>2</sub></em> = 0) and sharing the load equally (<em>F<sub>1</sub></em> = <em>F<sub>2</sub></em> = ½·<em>F<sub>TOT</sub></em>). Because microtubule growth is intrinsically variable, the two microtubules subsequently grow at different speeds. The computer then dynamically monitors the bead positions and adjusts the forces, <em>F<sub>1</sub></em> and <em>F<sub>2</sub></em>, according to the elastic coupling model. For purely elastic couplers, the force difference across the two microtubules equals the tip separation, (<em>x<sub>2</sub></em> – <em>x<sub>1</sub></em>), multiplied by the coupling stiffness (<em>κ</em>). When one microtubule grows more quickly than the other, tension on the leading (faster-growing) microtubule decreases, and tension on the lagging (slower-growing) microtubule increases to maintain a constant total force on the pair, <em>F<sub>TOT</sub></em>. For all experiments, <em>F<sub>TOT</sub></em> = 8 pN.
description: # Paired microtubules growing with a shared load
 [https://doi.org/10.5061/dryad.xksn02vnb](https://doi.org/10.5061/dryad.xksn02vnb) Our new dual-trap assay uses two separate laser trapping microscopes, located adjacent to one another in the same room and connected to a single computer. On each of the two instruments, we attach a kinetochore-decorated bead to a dynamic microtubule plus-end. The computer then simultaneously monitors and controls the forces on both microtubules. The computer adjusts the forces dynamically to simulate an elastic coupling of both plus-ends to a single shared load. We have simulated purely elastic couplers in these recordings, with stiffnesses of *κ* = 1 or 5 pN/um. To begin a dual-trap experiment, we first choose the spring stiffness, *κ*, and the total shared load, *F*<sub>TOT</sub>, which are kept constant. After a kinetochore-decorated bead is attached to a growing plus-end on each of the two instruments, feedback-control is initiated and the two plus-ends are arbitrarily considered to be parallel, with tips side-by-side (i.e., both at *x*<sub>1</sub> = *x*<sub>2</sub> = 0) and sharing the load equally (*F*<sub>1</sub> = *F*<sub>2</sub> = ½·*F*<sub>TOT</sub>). Because microtubule growth is intrinsically variable, the two microtubules subsequently grow at different speeds. The computer then dynamically monitors the bead positions and adjusts the forces, *F*<sub>1</sub> and *F*<sub>2</sub>, according to the elastic coupling model. The force difference across the two microtubules equals the tip separation, (*x*<sub>2</sub> – *x*<sub>1</sub>), multiplied by the coupling stiffness (*κ*). When one microtubule grows more quickly than the other, tension on the leading (faster-growing) microtubule decreases and tension on the lagging (slower-growing) microtubule increases to maintain a constant total force on the pair, *F*<sub>TOT</sub>. For all experiments, *F*<sub>TOT</sub> = 8 pN. 'Dual-trap_viewer_103124.pxp' displays microtubule plus end position vs time of each microtubule in a growing pair, labeled with the stiffness used to couple that pair. 'Raw' and re-smoothed force vs time data is also displayed for each microtubule (see details about re-smoothing under 'Data available without the use of Igor Pro 9'). In our most recent update, the user can now view either measured tip position or the tip position adjusted for system stiffness. Please see 'Update to dual-trap data and simulations.pdf' for details about how and why wanted to use tip position adjusted for system stiffness. This document also describes the correction of a minor bug affecting the tip separations of our simulated data, although this bug does not affect any of the files uploaded here and does not alter any conclusions of our publication. ## Code/Software To run the dual-trap data viewer, install the free trial of Igor Pro 9 at [https://www.wavemetrics.com/software/igor-pro-9](https://www.wavemetrics.com/software/igor-pro-9) and download 'Dual-trap_viewer_103124.pxp.' When you load this file, a front panel will appear and allow you to click through recordings of growing microtubule pairs using the 'Next Trace' and 'Previous Trace' buttons. Look at traces recorded with either soft or stiff couplers (*κ* = 1 or 5 pN/um) by clicking the up or down arrows to the right of 'Spring stiffness.' Use the checkboxes to look at measured tip position and/or tip position adjusted for system stiffness. See 'Dual-trap example document.docx' for the description of an example recording using this viewer. The Dual-trap_analysis.txt (available at [https://doi.org/10.5281/zenodo.8433109](https://doi.org/10.5281/zenodo.8433109)) contains functions we used to collect and organize dual-trap data, as well as to gather statistics about the time-dependent tip separation between microtubules in a pair. ## Data available without the use of Igor Pro 9 Additionally, each recording is saved in two separate .csv files, one with the measured tip positions reported in our original publication, the other with tip positions adjusted for system stiffness (please see 'Update to dual-trap data and simulations.pdf' for details about this adjustment). These files are available in folders within 'Individual_trace_data.zip.' The .csv files with raw tip positions contain 7 columns, the contents of which are listed below: 1. Measured tip position of microtubule 1 (in nm) 2. Measured tip position of microtubule 2 (in nm) 3. Smoothed force on microtubule 1 (in pN) -- smoothed from original data 4. Smoothed force on microtubule 2 (in pN) -- smoothed from original data 5. 'Raw' force on microtubule 1 (in pN) 6. 'Raw' force on microtubule 2 (in pN) 7. Time (in s) The smoothed forces in columns 3 and 4 are smoothed from the original data using a 0.5s smoothing window, so the first and last 0.25s of smoothed forces are affected by forces 0.25s before and after (respectively) the 'raw' forces in columns 5 and 6. This occasionally results in a small jump in force in the first or last 0.25s of the smoothed forces. Since this jump can affect our estimates of the initial force and thus the correction we need to apply to adjust for system stiffness, we performed the same smoothing using only the 'raw' forces in columns 5 and 6 and report these resmoothed forces in the .csv files described below. The .csv files with tip positions adjusted for system stiffness contain 4 columns, the contents of which are listed below: 1. Tip position of microtubule 1, adjusted for system stiffness (in nm) 2. Tip position of microtubule 2, adjusted for system stiffness (in nm) 3. Re-smoothed force on microtubule 1 (in pN) 4. Re-smoothed force on microtubule 2 (in pN) 'Dual-trap example document.docx' contains an example recording and summary statistics so that users can ensure that they are downloading and interpreting these files correctly. Finally, in Dual-trap assembly metadata.xslx, each row contains the following information about a given recording: 1. File name 2. Duration (in s) 3. How the event ended (detach, catastrophe, or other) 4. Average growth speed of microtubule 1 (in nm/s) 5. Average growth speed of microtubule 2 (in nm/s) 6. Estimated simulated spring constant (in pN/um) 7. How far ahead the microtubule tip was that started to disassembly (labeled 'catastrophe' and measured in nm, if applicable). Positive values indicate that the leading tip underwent catastrophe, while negative values indicate that the lagging tip underwent catastrophe. For recording 21_0906_044016, this pair probably used a stiff coupler because of the previous entry but the pair stayed too close together for the algorithm to tell. Other microtubule dynamics, such as average growth speed and catastrophe rate, were also measured for the entire population of soft or stiff couplers and are shown in this excel file. ## Change log **Update on 11/13/24:** We adjust our tip position recordings to account for series stiffness of our laser trap setup. Both raw and adjusted tip positions can now be downloaded or viewed using 'Dual-trap_viewer_103124.pxp.' Dual-trap_assembly_metadata.xlsx' does NOT use tip positions adjusted for series stiffness. We describe this update in detail in 'Update_to_dual-trap-data_and_simulations.pdf.' This document also describes the correction of a minor bug affecting the tip separations of our simulated data, although this bug does not affect any of the files uploaded here and does not alter any conclusions of our publication.