Fig. 8: Sources of error in vesicle models in STEPS.

a Vesicle diffusion: The percentage of diffusion steps that are over 2 vesicle diameters in length when the root mean square diffusion distance ranges from 0 to 2 vesicle diameters. b Bimolecular vesicle surface reactions with mobile cytosolic reactants: For different meshes representing the same 0.5 μm diameter spherical geometry, ranging from an average tetrahedron size of 120 nm (291 tetrahedrons) to 12.8 nm (265,307 tetrahedrons), the error in captured reaction rate is shown, when vesicles are stationary (blue line) or diffusing at 0.1 μm²s⁻¹ (orange line). The error is quantified by calculating the simulated rate by Supplementary Equation 6 and comparing to the expected rate (n = 1000 independent simulations for each mesh) c Error on the rate of second-order vesicle surface reactions when a cytosolic reactant is immobile. Since reactants are immobile and vesicles diffuse relatively slowly, one cannot use the integrated rate law as ground truth to estimate the error; instead, we consider the simulations at the smallest vesicle Δt = 10 μs as ground truth for the expected rate. In these simulations, vesicles diffuse at 0.1 μm²s⁻¹. The red line depicts the threshold on vesicle Δt from Supplementary Eq. (19). For each pair of average tetrahedron radius and vesicle Δt, the color in the heatmap denotes the error on the reaction rate estimated from the average concentration of reactants across n=20 independent simulations.