This source code simulates 2D diffusion (e.g. biological membrane components) under periodic boundary conditions in presence of a partially reflective meshgrid (e.g. actin membrane skeleton).

• N particles perform a random walk in 2D
• A meshgrid (repesenting a membrane skeleton) reflects particles, which can only pass with a probability p_jump
• 9 Gaussian shaped detection spots are placed on the membrane and simulated fluorescence traces are aquired
• The fluorescence traces are autocorrelated using the multiple tau algorithm, resulting in realistic fluorescence correlation spectroscopy (FCS) curves

The code was used to generate simulations published in a Biophysical Journal publication.

Lateral membrane diffusion modulated by a minimal actin cortex, Heinemann F., Vogel SK, Schwille P., 2013 (https://www.cell.com/biophysj/fulltext/S0006-3495(13)00260-9)

The simulation was optimized for performance using a profiler. It is written in C++ (with a small inline assembly part for a much faster floor computation).

The code should be easy to read (three files with lots of comments). I recommend starting with main(), then looking at CSimulatedDiffusion::start() where the simulation takes place.

• Scientists working on, or interested in FCS and / or diffusion
• Developers looking for example implementations of spatial hashing in C++ (a method for very fast collision detection, see https://conkerjo.wordpress.com/2009/06/13/spatial-hashing-implementation-for-fast-2d-collisions/).

Image: Simulated actin mesh, diffusing particles and 9 confocal detection spots.

• boost (https://www.boost.org/) (tested with the somewhat old: boost 1_48_0)
• cpp-yaml (https://github.com/jbeder/yaml-cpp)

• Tested under Windows 7 and 10 (should in principle also run under Linux)

1. Compile the project
2. Create file(s) decribing meshgrid (see mesh/1-2 mean82 sd31.txt)
3. Create / edit yaml file configuring the simulation
4. Open cmd, browse to project folder and run

simulated_diffusion.exe simulation_list.yaml

5. Drink some coffee and wait...
6. Analyze simulation results written to text files

The yaml file contains repeating blocks of 4 parameters. An example is in the repository. Example block:

voronoimesh: ./mesh/1-2 mean82 sd31.txt

resultfile: ./1-2 mean82 sd31_p001.txt

pjump: 0.01

Tmax: 100

Each block is one simulation and will output one result file. All blocks are computed until the end.

-voronoimesh: A text file with coordinates of the mesh. See example in repository. I used a custom program performing Voronoi tesselation (https://en.wikipedia.org/wiki/Voronoi_diagram), which I can distrubute on request.

-resultfile: Name of output file to write to. Output will be a simple textfile containing the 9 simulated FCS autocorrelation curves and their average.

-p_jump: Probability to cross a mesh fibre.

-Tmax: time in simulated seconds (I recommend 100-300s, with larger values for dense meshes and / or high pjump).

A simulated FCS curve (without mesh; with mesh the curve will move to right and a second component may appear, see paper https://www.cell.com/biophysj/fulltext/S0006-3495(13)00260-9).

CSimulatedDiffusion.cpp contains further physical and simulation parameters, which can be modified, e.g.:

• Diffusion coefficient: D (default: 10 µm²/s)
• Confocal spot size: r0 (default: 250 nm)
• Particle number: nParticles (default: 1000)

Try it out!