Running forward simulations - Epithelial / Mesenchymal Case Study

Use the forward simulator for the prescribed epithelial-mesenchymal case study; the learned emulator supports source-target shape assembly. Values are in model units; applications may supply external calibration for SI or biological interpretation. The active particle prefix can grow to a preallocated max_particles capacity. The simulation_with_autodiff tutorial walks through a complete run.

1. Allocate fixed-capacity Warp arrays for centers X, radii R, equilibrium radii R_eq, polarities P, activator A, inhibitor I, and cell types CT.

2. Relax geometry with simulator.mech_step_sticky. The mech_step_sticky_implicit variant uses local warp.grad for polarity, thickness, alignment, and optional WNT terms; soft-sphere derivatives remain explicit.

3. Pattern the activator and inhibitor fields by reaction-diffusion with simulator.chem_step, parameterized by chi (activator diffusivity relative to the inhibitor), gamma (reaction rate), and D_inhib (inhibitor diffusivity).

4. Grow cells with simulator.growth_step. Radii below their targets increase up to those targets; mesenchymal equilibrium radii are capped at R_max and epithelial equilibrium radii copy through.

5. Count neighbors and divide cells with simulator.count_neighbors_step, simulator.division_decision, and simulator.division_logic.

6. Write frames from the live Warp state with render.WarpMovieRenderer.write_frame_from_state (see Render trajectories).

Mechanics, chemistry, and growth write caller-supplied next-state arrays; growth also advances mesenchymal RNG keys. Division mutates shared state arrays and reserves unique daughter slots within capacity. Mesenchymal daughter radii conserve half volume; epithelial daughter radii copy.

Tip

Drop the particle count and the number of steps when you are validating a new environment.

For the equations behind these kernels — the soft-sphere force, the graph Laplacian, the activator-inhibitor reaction-diffusion system, the growth Hill function, and the division rules — see Forward and inverse modes and Emulator differentiability.