MultiMM: An OpenMM-based software for whole genome 3D structure reconstruction

MultiMM is an OpenMM model designed for modeling the 3D structure of the whole human genome. Its distinguishing feature is that it is multiscale, meaning it aims to model different levels of chromatin organization, from smaller scales (nucleosomes) to the level of chromosomal territories. The algorithm is both fast and accurate. A key feature enabling its speed is GPU parallelization via OpenMM, along with smart assumptions that assist the optimizer in finding the global minimum. One such fundamental assumption is the use of a Hilbert curve as the initial structure. This helps MultiMM to converge faster because the initial structure is already highly compacted.

After running the MultiMM model, users obtain a genome-wide structure. Users can color different chromosomes or compartments, or they can visualize individual chromosomes separately. MultiMM is simple to use, as it is based on modifying a single configuration file. Here we explain its usage.

The workflow of MultiMM is illustrated in the following schematic. The user first provides a set of interactions from a 3C-type experiment, representing chromatin loops, and optionally supplies compartment annotations. The user can also specify a region or chromosome of interest. MultiMM then imports an initial structure, performs basic preprocessing on the input data, and applies a force field corresponding to the provided interactions. All simulation parameters and user preferences must be specified in the config.ini file. Afterward, the software generates the 3D chromatin structures, and, if ATAC-Seq data are provided, applies nucleosome interpolation to refine the model.

Key Features

• OpenMM based.
• User-friendly software available via PyPI.
• Efficient simulation of chromatin interactions using 3D conformations.
• Can simulate the scales of nucleosomes, TADs, compartments, chromosomal territories and interactions with lamina. Scalable simulations across different force fields and resolution levels.
• Compatible with modern GPU-accelerated simulation libraries. CPU acceleration can also be done.
• Possibility of creation of ensembles of 3D structures of chromatin.

About Operating Systems

MultiMM has been tested primarily on Linux-based operating systems, with successful tests in Ubuntu, Debian, and Red Hat-based distributions. It is also possible to run it on macOS, though without CUDA support, which is helpful for accelerating computations. We do not recommend running MultiMM on Windows systems.

Installation

MultiMM can be easily installed with pip:

pip install MultiMM

PyPI software: https://pypi.org/project/MultiMM/.

Mathematical Model

We model chromatin as a coarse-grained polymer confined inside the nucleus. The system is described by an effective energy functional

$$E = E_{\text{pol}} + E_{\text{lamina}} + E_{\text{loop}} + E_{\text{block}}$$

Each bead represents a chromatin segment of fixed genomic length. The equilibrium structure is obtained by energy minimization or short relaxation dynamics.

Polymer Backbone

Polymer connectivity, stiffness, and excluded volume are enforced by the following potential energy terms:

$$ E_{\text{pol}} = E_{\text{bond}} + E_{\text{bend}} + E_{\text{rep}} $$

where

$$ E_{\text{bond}} = \sum_i k_b (r_{i,i+1} - \ell)^2 $$

is the harmonic bond potential that keeps consecutive beads at distance ≈ ℓ,

$$ E_{\text{bend}} = \sum_i k_s (\theta_i - \pi)^2 $$

is the bending energy that controls chain stiffness (θᵢ is the angle between bonds i−1→i and i→i+1),

and

$$ E_{\text{rep}} = \sum_{i < j} \epsilon \left( \frac{\sigma}{r_{ij}} \right)^\alpha $$

is the purely repulsive long-range interaction that enforces excluded volume.

The first term fixes bond lengths, the second controls bending rigidity, and the third prevents unphysical monomer overlap.

Looping Interactions

Chromatin loops detected experimentally are modeled as harmonic restraints

$$E_{\text{loop}} = k_\ell \sum_{(i,j)\in \text{loops}} (r_{ij} - d_{ij})^2 .$$

The equilibrium loop length depends on interaction strength $S_{ij}$ as

$$d_{ij} \propto S_{ij}^{-2/3}, \qquad d_{ij} \in [0.1, 0.2] .$$

For single cell data all loops have the same equilibrium distance.

Block Copolymer Compartmentalization

Long range compartmentalization is described by a Gaussian attraction between beads of the same compartment

$$ E_{\text{block}} = \sum_c E_c \exp\left(-\frac{r^2}{2 r_0^2}\right) $$

Only beads sharing the same compartment label interact. The interaction strength satisfies $|E_B| &gt; |E_A|$, enforcing stronger attraction for inactive chromatin. The interaction range is

$$r_0 = \frac{R_2 - R_1}{20}.$$

Subcompartments are treated by assigning distinct energy levels.

Nuclear Geometry and Lamina

Chromatin is confined between two concentric spherical boundaries with radii $R_1$ (nucleolus) and $R_2$ (lamina). Soft boundary conditions are imposed by

$$E_{\text{bc}} = C\bigl[\max(0,r-R_2)^2 + \max(0,R_1-r)^2\bigr].$$

B Compartment Lamina Attraction

Inactive compartments are attracted to the nuclear lamina via

$$ E_{Bl} = B \left( \sin^8 \frac{r-R_1}{R_2-R_1} - 1 \right) \left[ \delta(s+1) + \delta(s+2) \right] $$

This potential has minima near both inner and outer boundaries.

Chromosome Size Dependent Nucleolar Attraction

Smaller chromosomes experience a weak attraction toward the nucleolus

$$ E_G = G s_c \left( \sin\frac{r-R_1}{\ell_G} - \left(\frac{r-R_1}{\ell_G}\right)^2 \right) $$

where $s_c \in [0,1]$ encodes chromosome size ranking.

Optional Chromosome Globularization

When loop or compartment information is insufficient, an optional weak confining potential can be applied

$$E_{\text{chrom}} = \sum E_n \left(k_C r^4 - b r^3 + c r^2\right).$$

This term has no direct biological interpretation and is disabled by default.

Nucleosome Scale Interpolation

After coarse grained optimization, nucleosome positions are interpolated using a beads on the string zigzag model. Each nucleosome is represented as a helix with 1.65 DNA turns. The number of nucleosomes per bead is derived from normalized ATAC Seq signal, enforcing nucleosome rich regions in low accessibility chromatin.

Input Data

MultiMM relies on three types of datasets:

• Loop interactions in bedpe format (mandatory).
• Compartmentalization data in bed format (optional).
• ATAC-Seq p-value data in .BigWig format (optional).

Loops (bedpe file)

For loop interactions, users must provide a file describing interactions between anchor 1 and anchor 2, along with their strength.

The file must be in .bedpe format, contain 7 columns, and must not include a header.

chr10	100225000	100230000	chr10	100420000	100425000	95
chr10	100225000	100230000	chr10	101005000	101010000	56
chr10	101190000	101195000	chr10	101370000	101375000	152
chr10	101190000	101200000	chr10	101470000	101480000	181
chr10	101600000	101605000	chr10	101805000	101810000	152

The file can include interactions from all chromosomes; MultiMM will automatically handle them.

For single-cell data, users should prepare the file by setting the second and third columns identical (as well as the fifth and sixth columns) and set the strength value to 1.

Compartments

For (sub)compartment interactions, the file should be in the format produced by the CALDER software: https://github.com/CSOgroup/CALDER2. Users do not need to run CALDER specifically, but the file format must match. The file should contain at least the first four columns with chromosome, regions, and the subcompartment label. Example:

chr1	700001	900000	A.1.2.2.2.2.2.2	0.875	.	700001	900000	#FF4848
chr1	900001	1400000	A.1.1.1.1.2.1.1.1.1.1	1	.	900001	1400000	#FF0000
chr1	1400001	1850000	A.1.1.1.1.2.1.2.2.2.1	1	.	1400001	1850000	#FF0000
chr1	1850001	2100000	B.1.1.2.2.1.2.1	0.5	.	1850001	2100000	#DADAFF

Nucleosomes

For ATAC-Seq data, users must provide a BigWig file containing p-values. The pyBigWig library is required to read BigWig files. Note: pyBigWig is not compatible with Windows systems.

Definition of a region based on a gene (optional)

To model a genomic region around a specific gene, you can load a .tsv file containing gene information. Specify either the gene name or the gene ID.

The .tsv file should be formatted as follows:

gene_id	gene_name	chromosome	start	end
ENSG00000160072	ATAD3B	chr1	1471765	1497848
ENSG00000279928	DDX11L17	chr1	182696	184174
ENSG00000228037		chr1	2581560	2584533
ENSG00000142611	PRDM16	chr1	3069168	3438621
ENSG00000284616		chr1	5301928	5307394
ENSG00000157911	PEX10	chr1	2403964	2413797
ENSG00000269896		chr1	2350414	2352820
ENSG00000228463		chr1	257864	359681
ENSG00000260972		chr1	5492978	5494674
ENSG00000224340		chr1	10054445	10054781

In case that you specify the gene, MultiMM will output a visualization with the gene as well. For example, in the folowing region we can see the polymer structure that is modelled (around the gene) and the gene with red color.

The MultiMM model targets the gene file automatically, so you do not have to provide it. However, you can optionally change it.

Note: Currently, MultiMM is designed to work with human genome data. While it may be possible to run the code on other organisms with additional debugging and modifications, full support for other species is planned for future versions. MultiMM can process various types of datasets. It is capable of calling loops from a range of experiments, including Hi-C, scHi-C, ChIA-PET, and Hi-ChIP. However, we cannot guarantee that the default parameters are optimal for every dataset. Therefore, users are encouraged to test the software carefully and verify the convergence of the algorithm with their own data.Before adjusting any parameters, please read the method paper thoroughly to understand the role and impact of each force.

Usage

All the model's parameters are specified in a config.ini file. This file should have the following format:

[Main]

; Platform selection
PLATFORM = OpenCL

; Input data
FORCEFIELD_PATH = forcefields/ff.xml
LOOPS_PATH = /home/skorsak/Data/Rao/GSE63525_GM12878_primary+replicate_HiCCUPS_looplist_hg19.bedpe
COMPARTMENT_PATH = /home/skorsak/Data/Rao/subcompartments_primary_replicate/sub_compartments/all_sub_compartments.bed
ATACSEQ_PATH = /home/skorsak/Data/encode/ATAC-Seq/ENCSR637XSC_GM12878/ENCFF667MDI_pval.bigWig
OUT_PATH = application_note

; Simulation Parameters
N_BEADS = 50000
SHUFFLE_CHROMS = True
NUC_DO_INTERPOLATION = True

; Enable forcefield for genome-wide simulation
SC_USE_SPHERICAL_CONTAINER = True
CHB_USE_CHROMOSOMAL_BLOCKS = True
SCB_USE_SUBCOMPARTMENT_BLOCKS = True
IBL_USE_B_LAMINA_INTERACTION = True
CF_USE_CENTRAL_FORCE = True

; Simulation Parameters
SIM_RUN_MD = True
SIM_SAMPLING_STEP = 50
SIM_N_STEPS = 1000
TRJ_FRAMES = 100

After specifying the parameters and forces, users can run the following command in the terminal:

MultiMM -c config.ini

The software will output a folder with the resulting structure and plots showing compartment distribution.

Example data can be found on Google Drive: https://drive.google.com/drive/folders/1nFAPE4pCaHpeL5nw6nq0VvfUFoc24aXm?usp=sharing. Note that this data is publicly available from Rao et al. The subcompartment predictions were made using CALDER, and the ATAC-Seq data is from ENCODE.

In the examples folder, we provide example configuration files for different modeling scenarios.

Helper argument based on modelling levels

In the latest version of MultiMM, we have introduced the MODELLING_LEVEL argument. This is a magic parameter designed to help users—especially those new to molecular modelling—easily configure model parameters based on the desired resolution.

The following modelling levels are available:

• GENE: The user provides a gene of interest along with a .bedpe file path. MultiMM then models the gene using a default (+- 100kb) gene_window . At this level, compartment forces are not considered.

• REGION: The user specifies a chromosome and genomic coordinates. Compartment interactions can also be included optionally. MultiMM models only the selected genomic region.

• CHROMOSOME: The user specifies a chromosome number, and MultiMM determines the start and end coordinates internally. Compartment data can also be imported.

• GW (Genome-Wide): This option models the entire genome. No input for chromosome or coordinates is needed. This is the most computationally intensive option and may take from minutes to hours, depending on the hardware.

Additionally, this argument automatically sets the number of simulation beads. Regardless of the user-defined N_BEADS value, specifying MODELLING_LEVEL overrides it with a default setting:

• GENE: 1,000 beads
• REGION: 5,000 beads
• CHROMOSOME: 20,000 beads
• GW: 200,000 beads

This feature offers a convenient starting point for new users. Nevertheless, we recommend that advanced users avoid using this argument if they require finer control over simulation parameters.

Vizualization

For vizualization purposes, if you would like to import the whole genome structure you may use the command,

import simulation.plots as splt

splt.viz_chroms(sim_path)

For sim_path you should add the output folder directory path (add comps=Fase in case that you do not need compartment coloring). Otherwise, in case that the user would like to model a particular region, without using compartment or chromosome coloring (pretty much any cif structure), they can type,

import simulation.plots as splt
import simulation.utils as suts

V = suts.get_coordinates_cif(cif_path)
splt.viz_structure(V)

We would like once again to thank people who developed pyvista library and allow us to have fast and good vizualizations of large chromatin structure.

Simulation Arguments

MultiMM has numerous configurable parameters. Below is a description of each argument and its default values. The defaults have been tested for genome-wide simulation but can be modified in the configuration file if needed. Units are typically assumed based on OpenMM conventions, though explicit unit specification is not required.

Here we can see the long table of the simulation arguments. Somtimes MultiMM might not work for some choices of arguments. For example:

• If you would like to model lamina interaction having disabled compartment interactions.
• If you do not provide appropriate data i.e. for compartmentalization but you have enabled (sub)compartent-specific forcefield.

Therefore, it is advisable to read the paper and understand well the meaning of each force before you start running simulations. MultiMM is a research model, not a market product and thus it requires a level of expertise (despite the easiness of usage) to underatand and run it.

Simulation Arguments

Below is a categorized description of the simulation arguments and their default values. These parameters can be modified in the configuration file as needed.

Platform and Device Configuration

Argument Name	Type	Value	Units	Description
PLATFORM	str	CPU	None	Name of the platform. Available choices: CPU, OpenCL, CUDA.
CPU_THREADS	int	None	None	Number of CPU threads (if CPU is chosen as the platform).
DEVICE	str	None	None	Device index for CUDA or OpenCL (count from 0).

Input and Output

Argument Name	Type	Value	Units	Description
FORCEFIELD_PATH	str	None	None	Path to XML file with forcefield.
LOOPS_PATH	str	None	None	Path to .bedpe file with loops (required).
COMPARTMENT_PATH	str	None	None	Path to .bed file with subcompartments from CALDER.
ATACSEQ_PATH	str	None	None	Path to .bw or .BigWig file with ATAC-Seq data (optional).
OUT_PATH	str	results	None	Output folder name.
INITIAL_STRUCTURE_PATH	str	None	None	Path to CIF file for the initial structure.
GENE_TSV	str	None	default_path	Path to a .tsv file with gene locations in the genome.
GENE_NAME	str	None	None	Name of the gene of interest.
GENE_ID	str	None	None	ID of the gene of interest.

Initial Structure Configuration

Argument Name	Type	Value	Units	Description
BUILD_INITIAL_STRUCTURE	bool	True	None	Whether to build a new initial structure.
INITIAL_STRUCTURE_TYPE	str	hilbert	None	Type of initial structure. Options: hilbert, circle, rw, confined_rw, self_avoiding_rw, helix, spiral, sphere, knot.

Modelling Levels and Regions

Argument Name	Type	Value	Units	Description
MODELLING_LEVEL	str	None	None	Specify resolution: 'GENE', 'REGION', 'CHROM', or 'GW'.
LOC_START	int	None	None	Starting coordinate for the region of interest.
LOC_END	int	None	None	Ending coordinate for the region of interest.
CHROM	str	None	None	Chromosome for the region of interest.
GENE_WINDOW	int	10000	bp	Window size around the gene of interest.

Simulation Parameters

Argument Name	Type	Value	Units	Description
N_BEADS	int	50000	None	Number of simulation beads.
SHUFFLE_CHROMS	bool	False	None	Shuffle chromosomes.
SHUFFLING_SEED	int	0	None	Random seed for shuffling.
SIM_RUN_MD	bool	False	None	Whether to run MD simulation.
SIM_N_STEPS	int	10000	None	Number of MD simulation steps.
SIM_SAMPLING_STEP	int	100	None	Number of steps between saved structures.
SIM_TEMPERATURE	Quantity	310	kelvin	Simulation temperature.
SIM_INTEGRATOR_TYPE	str	langevin	None	Integrator type: variable_langevin, langevin, variable_verlet, verlet, amd, brownian.
SIM_INTEGRATOR_STEP	Quantity	1	fsec	Step size for the integrator.
SIM_FRICTION_COEFF	float	0.5	1/psec	Friction coefficient (for Langevin and Brownian integrators).
SIM_SET_INITIAL_VELOCITIES	bool	False	None	Set initial velocities based on Boltzmann distribution.
TRJ_FRAMES	int	2000	None	Number of trajectory frames to save.

Forcefield Parameters

Argument Name	Type	Value	Units	Description
POL_USE_HARMONIC_BOND	bool	True	None	Use harmonic bond interaction for consecutive beads.
POL_HARMONIC_BOND_R0	float	0.1	nm	Equilibrium distance for harmonic bonds.
POL_HARMONIC_BOND_K	float	300000.0	kJ/mol/nm^2	Force constant for harmonic bonds.
POL_USE_HARMONIC_ANGLE	bool	True	None	Use harmonic angle interaction for consecutive beads.
POL_HARMONIC_ANGLE_R0	float	pi	radians	Equilibrium angle for harmonic angle force.
POL_HARMONIC_ANGLE_CONSTANT_K	float	100.0	kJ/mol/radian^2	Force constant for harmonic angles.
EV_USE_EXCLUDED_VOLUME	bool	True	None	Use excluded volume interaction.
EV_EPSILON	float	100.0	kJ/mol	Strength of excluded volume interaction.
EV_R_SMALL	float	0.05	nm	Small radius added to avoid singularities.
EV_POWER	float	3.0	None	Exponent for excluded volume potential.

Advanced Features

Argument Name	Type	Value	Units	Description
SC_USE_SPHERICAL_CONTAINER	bool	False	None	Use a spherical container.
SC_RADIUS1	float	None	nm	Inner radius of the spherical container.
SC_RADIUS2	float	None	nm	Outer radius of the spherical container.
SC_SCALE	float	1000.0	kJ/mol/nm^2	Scaling factor for the spherical container.
CHB_USE_CHROMOSOMAL_BLOCKS	bool	False	None	Use chromosomal blocks.
CHB_KC	float	0.3	nm^(-4)	Block copolymer width parameter.
CHB_DE	float	1e-5	kJ/mol	Energy factor for chromosomal blocks.
SCB_USE_SUBCOMPARTMENT_BLOCKS	bool	False	None	Use subcompartment blocks.
SCB_DISTANCE	float	None	nm	Equilibrium distance for subcompartment blocks.
SCB_EA1	float	1.0	kJ/mol	Energy strength for A1 compartment.
SCB_EA2	float	1.33	kJ/mol	Energy strength for A2 compartment.
SCB_EB1	float	1.66	kJ/mol	Energy strength for B1 compartment.
SCB_EB2	float	2.0	kJ/mol	Energy strength for B2 compartment.
IBL_USE_B_LAMINA_INTERACTION	bool	False	None	Enable interactions of B compartment with lamina.
IBL_SCALE	float	400.0	kJ/mol	Scaling factor for lamina interaction.
CF_USE_CENTRAL_FORCE	bool	False	None	Enable attraction of smaller chromosomes to the nucleolus.
CF_STRENGTH	float	10.0	kJ/mol	Strength of central force attraction.

Ensemble Generation

Argument Name	Type	Value	Units	Description
GENERATE_ENSEMBLE	bool	False	None	Generate an ensemble of structures.
N_ENSEMBLE	int	None	None	Number of structures in the ensemble.
DOWNSAMPLING_PROB	float	1.0	None	Probability of downsampling (0 to 1).

Nucleosome Parameters

Argument Name	Type	Value	Units	Description
NUC_DO_INTERPOLATION	bool	False	None	Enable nucleosome interpolation.
NUC_RADIUS	float	0.1	None	Radius of the nucleosome helix.
POINTS_PER_NUC	int	20	None	Number of points in a nucleosome helix.
PHI_NORM	float	pi/5	None	Zig-zag angle for nucleosome helix.

Output Directory

The output directory is organized in the following folders,

config_auto.ini
├── md_frames
│   ├── frame_1_100.cif
├── metadata
│   ├── chimera_gene_coloring.cmd
│   ├── chrom_idxs.npy
│   ├── chrom_lengths.npy
│   ├── ds.npy
│   ├── ms.npy
│   ├── MultiMM_annealing.dcd
│   ├── MultiMM_init.cif
│   ├── MultiMM.psf
│   ├── ns.npy
│   └── parameters.txt
├── model
│   ├── MultiMM_afterMD.cif
│   └── MultiMM_minimized.cif
├── plots
│   ├── initial_structure_gene_coloring.png
│   ├── initial_structure.png
│   ├── minimized_structure_gene_coloring.png
│   ├── minimized_structure.png
│   ├── structure_afterMD_gene_coloring.png
│   └── structure_afterMD.png

In md_frames, the frames of md dynamics can be found in case that md simulation is enabled.

In metadata you can find the initial structure and other produced numpy arrays. For example, ms, ns, are the left and right locations of loops in the region of interest. ds is the loop strength converted to distance. psf and dcd files are for the visualization of the trajectory in UCSF chimera software: https://www.cgl.ucsf.edu/chimera/, and chimera_gene_coloring.cmd is genetrated to give the coloring with the red region to be the gene of interest.

In the model is the resulted minimized structure and the structure after the MD simulation. If it is genomewide simulation, it would output the structures of each chromosome in a folder chromosomes.

In plots directory you can find plots of the structures. Note that the initial structure plot is only to see the initial stucture used in the simulation. Initial structure does not have direct biological meaning.

Citation and Contribution

The software is freely distributed under the GNU license and is available for use in research, in accordance with the open-source license of MultiMM. If you use the software for research or other purposes, please cite the following paper:

• Korsak, Sevastianos, Krzysztof Banecki, and Dariusz Plewczynski. "Multiscale molecular modeling of chromatin with MultiMM: From nucleosomes to the whole genome." Computational and Structural Biotechnology Journal 23 (2024): 3537–3548.

If you would like to contribute to the development of this model or suggest improvements, we encourage you to contact the authors. Additionally, if you encounter any issues while running the software, your feedback is highly appreciated, and we are happy to assist you.