Simulation of cytokinetic rings in isolated fission yeast protoplasts

Simulation of a fully three-dimensional coarse-grained mathematical model of the fission yeast cytokinetic ring is presented here. The goal is to observe a stable, tense ring under normal conditions and to investigate ring phenotypes when component turnover is absent. A brief overview of the simulation follows. For complete details, refer to the Results and the Methods section of https://www.biorxiv.org/content/10.1101/2021.03.18.436017v1 or later version(s) if available. Please cite this preprint or a peer-reviewed, published version whichever is later if you use the software in your research.

The simulation has four components - the myosin-II molecule Myo2, actin filaments, the formin Cdc12, and the actin crosslinker alpha-actinin. The first three components are represented as beads whereas the last is represented as a simple spring. Myo2 and Cdc12 molecules are anchored to the plasma membrane, represented as the inner surface of a cylinder of fixed radius. They can slide along the membrane, maintaining fixed distances from it, and experience a drag force from the membrane. One bead of myosin represents an anchored cluster of 16 heads. One actin bead represents a 100 nm stretch of actin.

Force producing interactions in the simulation are: a myosin cluster binding actin filament(s) with a capture force, myosin clusters exerting pulling forces on actin filaments along their length and dependent on their relative velocity, actin crosslinking forces, actin bending forces, drag forces from the cytosol, lateral and perpendicular forces from the membrane on anchored components, excluded volume forces between myosins, and restoring forces that push straying components back into the interior of the cylinder. Components evolve according to first-order dynamics.

On and off rates of Myo2, Cdc12, alpha-actinin, the actin synthesis rate, and the actin severing rate produced by cofilin are all tuned to faithfully reproduce experimentally measured amounts and turnover times. After 10 minutes of ring simulation, dissociation rates can be greatly reduced and association rates abolished to investigate ring phenotypes in the absence of turnover.

A brief overview of the MATLAB files follows. Simulation can be run using the Slurm workload manager on a computing cluster using runv9Terre.sh, or standalone simulations can be initiated using the command task_yeti(num) where num is supplied as the seed to the random number generator.

Filename | Description --- | --- bmnbr.m | Identify which myosin cluster interacts with which actin bead geta.m | Construct one part of the drag matrix for first-order dynamics getforce.m | Calculate forces on all simulation components getm.m | Construct the other part of the drag matrix for first-order dynamics getpcpqxy.m | Calculate derivatives of constraint equations getrdiff.m | Obtain vectors along actin filament lengths initialcirclerand.m | Initialize the ring parametersv7.m | Set parameters for the simulation ptcap.m | Adjust which actin bead interacts with which myosin cluster rk1.m | Organizing script that executes each part of the simulation in order runposzcyl.m | Set some more simulation parameters and initialize the ring, discarding defective initial conditions runv9Terre.sh | Shell script to execute the simulation using a Slurm workload manager stallforcepf.m | Calculate forces exerted by myosin clusters taskyeti_v9.m | Called by runv9Terre. Main coordinating script that executes many cycles of rk1 and saves output data from each cycle. update.m | Adjust ring component numbers velocity.m | Obtain constraint forces and component velocities

Henceforth are the analysis scripts in the analysis/ folder.

Filename | Description --- | --- tensvstime.m | Calculate tension vs time for a set of runs tensioncirc.m | Helper script of tensvstime.m getsegtens.m | Helper script of tensvstime.m gettensring.m | Helper script of tensvstime.m runv9TerreTiffCreate.sh | Shell script to generate TIFF files from simulation outputs using a slurm manager ringplotpreparetiff.m | Main coordinating script to generate TIFF files fluoemumyo.m | Generate one frame of a TIFF file corrlenvstimesim.m | Calculate correlation function for a set of runs corrcalcCirc.m | Helper script of corrlenvstimesim.m corrlenvstimeexpt.m | Calculate correlation function for experimental kymographs corrcalc.m | Helper script of corrlenvstimeexpt.m trackaggregates.m | Script to plot mean distance b/w aggregates vs time, both simulation and experiment stplotring2d3feb21.m | Plot the simulated ring makekymo.ijm | Fiji macro to make kymographs. prom2.roi | Region of interest (ROI) used by Fiji macro to make kymographs.

Notes

1. Use make_kymo.ijm with prom2.roi and fake confocal images created from simulation data to generate kymographs.
2. Use makekymo.ijm with the respective ROI file and the respective real confocal image from experiment to generate real experimental kymographs. The width parameter in makekymo.ijm may have to be adjusted, but it is usually in the range 10-18.