Diffusion-Interaction Simulation

Overview

The Diffusion-Interaction module simulates dynamic molecular processes including diffusion and interactions between particles in a controlled environment. This allows you to model realistic molecular behaviors such as:

• Free diffusion of monomers
• Formation of molecular complexes (dimers)
• Dissociation of complexes
• Combined translational and rotational diffusion

The simulation operates within a defined box with customizable physical parameters, making it suitable for studying a wide range of biological phenomena at the single-molecule level.

Simulation Model

The diffusion simulation is based on the Smoluchowski dynamics model with the following components:

1. Particles: Represented as point particles (monomers) or rigid structures (dimers)
2. Diffusion: Isotropic Brownian motion with specified diffusion coefficients
3. Reactions:
   • Association: Two monomers within reaction radius form a dimer
   • Dissociation: Dimers break with rate k_off
4. Boundaries: Periodic or reflecting boundary conditions

At each time step, the simulation:

• Updates molecular states (dimerization/dissociation)
• Updates positions with appropriate diffusion models
• Handles boundary conditions

Physical Units

All simulation parameters use consistent physical units:

• Spatial dimensions: microns (μm)
• Time: seconds (s)
• Diffusion coefficients: μm²/s
• Rate constants: s⁻¹

Getting Started

Running a Basic Simulation

The main interface for running diffusion simulations is the simulate function with DiffusionSMLMParams:

using SMLMSim

# Set simulation parameters
params = DiffusionSMLMParams(
    density = 0.5,        # molecules per μm²
    box_size = 10.0,      # μm
    diff_monomer = 0.1,   # μm²/s
    diff_dimer = 0.05,    # μm²/s
    k_off = 0.2,          # s⁻¹
    r_react = 0.01,       # μm
    d_dimer = 0.05,       # μm
    dt = 0.01,            # s
    t_max = 10.0          # s
)

# Run the simulation
smld = simulate(params)

The smld output is a BasicSMLD structure containing all emitters across all time points, with each emitter having frame information corresponding to the camera settings.

Simulation Parameters

The DiffusionSMLMParams structure allows you to customize various aspects of the simulation:

# More complex simulation
params = DiffusionSMLMParams(
    density = 2.0,           # Higher density
    box_size = 20.0,         # Larger area
    diff_monomer = 0.2,      # Faster monomer diffusion
    diff_dimer = 0.08,       # Faster dimer diffusion
    diff_dimer_rot = 1.0,    # Faster rotational diffusion
    k_off = 0.05,            # Slower dissociation (more stable dimers)
    r_react = 0.015,         # Larger reaction radius
    d_dimer = 0.08,          # Larger dimer separation
    dt = 0.005,              # Smaller time step (higher precision)
    t_max = 30.0,            # Longer simulation
    ndims = 2,               # 2D simulation (default)
    boundary = "periodic",   # Periodic boundaries (default)
    camera_framerate = 20.0, # Camera frames per second
    camera_exposure = 0.04   # Camera exposure time
)

Microscope Image Generation

The diffusion simulation can be converted into realistic microscope images using point spread function models.

Creating Images from Simulation Data

# Set up camera and PSF
pixelsize = 0.1  # 100nm pixels
pixels = Int64(round(params.box_size/pixelsize))
camera = IdealCamera(1:pixels, 1:pixels, pixelsize)

# Set up PSF (Gaussian with 150nm width)
using MicroscopePSFs
psf = MicroscopePSFs.GaussianPSF(0.15)  # 150nm PSF width

# Generate images
image_stack = gen_images(smld, psf;
    photons=1000.0,
    bg=5.0,
    poisson_noise=true
)

Analyzing Results

Extracting Dimers

To focus on the behavior of dimers, you can extract only the molecules in dimer state:

# Extract dimers from the full simulation
dimer_smld = get_dimers(smld)

Analyzing Dimer Formation

To quantify the formation of dimers over time:

# Calculate fraction of molecules in dimer state
frames, dimer_fractions = analyze_dimer_fraction(smld)

# Plot dimer formation over time
using CairoMakie
fig = Figure()
ax = Axis(fig[1, 1],
    xlabel="Frame",
    ylabel="Fraction of molecules in dimers",
    title="Dimer formation dynamics"
)
lines!(ax, frames, dimer_fractions)
fig

Emitter Types

The diffusion module introduces specialized emitter types:

• DiffusingEmitter2D: 2D emitter with state information (monomer/dimer)
• DiffusingEmitter3D: 3D emitter with state information (monomer/dimer)

These types include additional properties:

• timestamp: Actual simulation time
• state: Molecular state (:monomer or :dimer)
• partner_id: ID of linked molecule (for dimers)