Fig. 1

Conceptual overview of Cell4D. A Screenshot of the Cell4D graphical interface. For further details on the interface see the project GitHub: https://github.com/ParkinsonLab/cell4d. B Model design interface. A web interface for creating and editing Cell4D model files. Custom XML model files can be loaded in by a user, or a preset example model can be selected. Once a model is loaded in, parameters of the model will automatically fill the text boxes in the interface. Users can edit the model by modifying the text in each textbox; real-time error messages will appear to prevent invalid inputs from being added. When the “Save” button on the bottom is pressed, if no textboxes have invalid inputs, the information in the text boxes of the current active tab will be saved to the loaded model. Users can switch between tabs that contain different model information such as modifying compartment spaces, molecular species, and reactions. Once all changes are saved on each tab, the user can click “Save model” on the top banner to download the loaded model onto their local device. C Simulation set up and flow time cycle logic. Parameters that describe system behavior such as how molecules behave within the simulation space as well as the way they interact with other molecules are described in an XML input file, which is then used to initialize the simulation space. The simulation then cycles through a series of steps until the end condition is met. Output occurs in two forms: tab-delimited files (.tsv) of molecule counts at each time step, and particle logs recording the position and state information of molecules in the simulation. D Diffusion of bulk molecules shown for a single voxel. At each time step, a portion of the bulk molecules for each c-voxel will diffuse into a neighboring c-voxel, based on the current concentration and the molecule’s diffusion rate constant. This is calculated for all c-voxels at every timestep. (i) an initial setup where a c-voxel contains 100 molecules (orange) with three adjacent voxels that contain 5 molecules each (blue). Diffusion of molecules into grey voxels are disabled in this example. (ii) bulk molecule diffusion calculation is done for each voxel which depends on the system timestep length setting and the concentration of molecules in each voxel. (iii) image shows the concentration of molecules in each voxel after one timestep. E Implementation of off-lattice movement of point particles. (i) and (ii) show the diffusion path of the reactant (blue) after 1 µs for 0.2 µs and 1 µs timestep systems respectively. In (i), using 0.2 µs timesteps, the particle was able to enter the reaction radius of the first reactant (red) which would allow a reaction to occur. In (ii), using 1 µs timesteps, although the final diffusion path of the particle remains the same, there is no step where the second reactant has an opportunity to react with the first reactant.To avoid such cases Cell4D implements the Andrews-Bray-adjustment to artificially increase reaction radii of molecules according to the size of the time step (iii and iv) [26]