Active loop extrusion simulation on a single polymer chain

Brian Chan, Rubinstein lab, Duke University (2023)

This document will instruct you how to compile and run a hybrid Molecular Dynamics - Monte Carlo (MD-MC) simulation code for steady state active loop extrusion on a single polymer chain.

See the preprint:

B. Chan and M. Rubinstein, Activity-driven chromatin organization during interphase: compaction, segregation, and entanglement suppression. bioRxiv (2024). https://www.biorxiv.org/content/10.1101/2024.01.22.576729v1

Update- paper is now published: https://www.pnas.org/doi/10.1073/pnas.2401494121

Prerequisites

The main pieces of code are ExtrSim.c and ExtrSim_MoreOutputs.c. The codes use LAMMPS (23Jun2022 version) as a C library and MPI for parallelization. To compile this code, you must first build LAMMPS as a shared library (see LAMMPS documentation https://docs.lammps.org/Build_link.html). You must also ensure that the caller code can find the library, which may require editing your environemntal variables. Note that this code was tested with OpenMPI 4.1.1.

Compilation

Once LAMMPS is built as a shared library, make sure that the following files are in your working directory:

Makefile will compile the code, after appropriate modifications.
ExtrSim.c is the main code with active loop extrusion.
ExtrSim_MoreOutputs.c is the same simulation but generates additional output files.

Before compiling the code, load your MPI implementation, for example with module load OpenMPI/4.1.1 or something similar. Make sure you use the same MPI implementation used for building LAMMPS.

Then, compile with make ExtrSim. Note that the Makefile will need to be modified to fit your specific machine and directory structure. Specifically, the following snippets could be changed:

CC=mpicc to fit your C compiler
/path/to/LAMMPS/src/ to specify the path of the LAMMPS src directory
-llammps_mpi to specify the name and/or path of the LAMMPS shared library. In this case, the LAMMPS library was called liblammps_mpi.so and its path was in the LD_LIBRARY_PATH environment variable.

There should now be an executable called ExtrSim in your working directory.

Running a simulation

Ensure that your working directory has the following files:

in.FirstSteps is a LAMMPS input file used for initial MD setup.
data.InitConformation is the LAMMPS data file with the initial chain conformation
ExampleSubmission.joblst is a barebones example submission script for a SLURM scheduler. This will depend on the machine on which you run the simulation.

You will need to load the MPI implementation. Then, run a simulation with the following command:

mpirun -n <NTASKS> ./ExtrSim <MaxCoh> <p_jump> <NumBeads> <NumMCSteps> <outputfileSuffix> <K_coh> <R0_coh> <MDtauperMC> <MDtauperdump> <WorkPath> <InitialData> <InitialMDTau> <t_int> <bindsite> <r_c> <printR2contfrequency> <ring> <RandSeed> <p_on> <p_off> <stopfilename> <NumberOfStops>

All but the last two arguments are required.

<NTASKS> is the number of MPI tasks that you are using.
<MaxCoh> is the maximum number of extruders allowed to be simultaneously bound to the polymer chain. Usually set this to a number 4-5 times the expected average number of bound cohesins.
<p_jump> this is the probability of cohesin domains passing/traversing each other. 1 means unimpeded. 0 means fully impeded.
<NumBeads> is the number of beads in the simulation
<NumMCSteps> is the number of MC steps you want to run for
<outputfileSuffix> is the suffix you want to be appended to all of your output files
<K_coh> is the spring constant of the cohesin bond. Usually set to 1.
<R0_coh> is the max length of the cohesin bond. Usually set to 4.
<MDtauperMC> is the ratio of MD tau (Lennard Jones time) to MC steps. We usually use 5. This sets the average extrusion velocity.
<MDtauperdump> is how frequently you want to dump out bead coordinates in units of MD Tau. Usually we use 1, 5, or 10.
<WorkPath> is the path to the directory you want all of the output files to go
<InitialData> is the initial data file. Use data.InitConformation
<InitialMDTau> is the number of MD tau you want to run before starting extrusion.
<t_int> is the integration time step for MD. Typically use 0.01.
<bindsite> is the bead index of cohesin binding, if needed. Set it to 0 for nonspecific binding.
<r_c> is the minimum distance between beads considered for contact, in units of MD simulation distance units (Lennard Jones sigma). Typically use something close to 1.5.
<printR2contfrequency> is how frequently you want to print the contact matrix and internal mean square distances for the chain (units of MC steps).
<ring> should be 0 if you are simulating a linear chain, 1 if you are simulationg a ring. Usually set to 0.
<RandSeed> is the seed used for the random number generator.
<p_on> is the probability that a cohesin binds a bead during one MC timestep. This is the probability per bead
<p_off> is the probability that a cohesin unbinds during one MC timestep. This is the probability per bound cohesin
<stopfilename> is the name of the file that has the TAD anchors/stop signs. Not necessary if there are no anchors. The file stopfile.txt has an example with TAD anchor pairs at beads (1,200) and (500,700).
<NumberOfStops> is the number of TAD anchor/stop sign pairs. Not necessary if there are no anchors.

Outputs

This code will have several output files that will be in <WorkPath>. Each will end in the <outputfileSuffix> of your choosing.

Status....txt has some input information and provides status updates (when the simulation is 25%, 50%, 75% done).
NumCoh....txt prints the number of cohesins bound to the chain every step
Acc....txt has four columns. The first column is the number of attempted moves made by a left cohesin domain. The second column is the number of accepted moves. The 3rd and 4th are the same, but for a right cohesin domain. Each column is a running sum.
Bind....txt has three columns. The first two are the bead indices at which a cohesin bound the chain, and the third is the MC step at which a cohesin bound the chain
FinalLife....txt has two columns. The first column is the residence time of a cohesin when it unbinds (in MC steps). The second column is the loop length when it unbinds
coordsLEUnwrap....txt has the coordinates of the chain formatted as a LAMMPS dump file with unwrapped coordinates.
Contacts....txt has the number of conformations in which two beads were within the cutoff distance r_c. First column is bead i, second column bead j, third column is number of contacts.
R2....txt has the mean squared distance between beads i and j, organized like Contacts....txt.
ReeRg....txt has 5 columns. The time step (in units of MD integration steps), the end to end vector (x,y,z components), and the radius of gyration. This is calculated and printed out from LAMMPS with the same frequency as bead coordinates.
LogInit...txt is the LAMMPS log file from the in.FirstSteps input script. LAMMPS log outputs are suppressed once extrusion starts.

If you compile and run ExtrSim_MoreOutputs.c, additional output files will be generated:

CohLocs...txt has 2*T rows, where T is the number of MC steps. Each column shows the bead indices to which an extruder is bound. Ex., [1 10 50; 100 32 52] means three extruders were bound, one at beads 1-100, one at 10-32, and one at 50-52.
CohLife...txt has T rows, where T is the number of MC steps. Each column shows the current residence time of a given cohesin (in units of MC steps). The columns correspond to the same cohesins as the columns in the previous file. Using the same example above, if this file reads [90 40 2], then the cohesin currently at beads 1-100 has been bound to the chain for 90 MC steps, the cohesin at 10-32 has been bound for 40 MC steps, and the cohesin at 50-52 has been bound for 2 steps.
CohLocsEach_<Suffix>_<LoopNumber>.txt is similar to the CohLocs...txt file, but it only contains the bead indices to which a single extruder is bound. Each line is a new MC step. The <LoopNumber> increases as more cohesins bind to the chain, meaning there could be hundreds or thousands of these files by the end of a long simulation.
CohFluc_<Suffix>_<LoopNumber>.txt is similar to the previous file, but instead records the center of mass of the cohesin bond (x,y,z components). Each line is a new MC step.

Additional information

The ExampleSubmission.joblst file has an example for how to start a simulation on an HPC system with a SLURM scheduler. The data.InitConformation file has the conformation of a single linear Kremer-Grest bead-spring polymer with 1000 beads. Note that two bond styles are used: the standard FENE bond a softer FENE bond to represent cohesin. in.FirstSteps is a LAMMPS input file used by the full simulation to run ${InitSteps} molecular dynamics integration steps before extrusion starts, where ${InitSteps} is <InitialMDTau>/<t_int> from the simulation parameters dictated by the user at runtime. This LAMMPS input file specifices a theta-like implicit solvent (if there was no extrusion) using a Lennard-Jones pair potential between beads.