FIGURE 3:

Reversible bimolecular reactions provide fundamental building blocks for any complex biological systems and thus warrant careful testing. In all dimensions, we use well-mixed initial conditions in closed systems, such that the reactions will reach a well-defined thermodynamic equilibrium. We test them using the nonspatial ODE and SSA methods, which match each other for all systems. The analytical solution to the rate equation is essentially exactly captured by the ODE. We compare the spatial PDE solved using VCell with single-particle methods solved via the FPR algorithm (NERDSS) and Smoldyn. For the 3D→2D reaction, we see the first difference between the ODE and PDE solution, because in the spatial models the reactants are well mixed in distinct locales (volume vs. surface), whereas in the nonspatial models, they are all well mixed in one volume. For 2D, single-particle methods will differ from other approaches, with NERDSS essentially capturing the theoretical diffusion-influenced reaction dynamics in 2D (Yogurtcu and Johnson, 2015a).