  Biochemical reactions typically occur at low copy numbers, but at once in
crowded and diverse environments. Space and stochasticity therefore play an
essential role in biochemical networks. Spatial-stochastic simulations have
become a prominent tool for understanding how stochasticity at the microscopic
level influences the macroscopic behavior of such systems. However, while
particle-based models guarantee the level of detail necessary to accurately
describe the microscopic dynamics at very low copy numbers, the algorithms used
to simulate them oftentimes imply trade-offs between computational efficiency
and accuracy. eGFRD (enhanced Green's Function Reaction Dynamics) is an exact
algorithm that evades such trade-offs by partitioning the N-particle system
into M<N analytically tractable one- and two-particle systems; the analytical
solutions (Green's functions) then are used to implement an event-driven
particle-based scheme that allows particles to make large jumps in time and
space while retaining access to their state variables at any moment. Here we
present "eGFRD2", a new eGFRD version that implements the principle of eGFRD in
all dimensions, enabling efficient simulation of biochemical reaction-diffusion
processes in the 3D cytoplasm, on 2D planes representing membranes, and on 1D
elongated cylinders representative of, e.g., cytoskeletal tracks or DNA; in 1D,
it also incorporates convective motion used to model active transport. We find
that, for low particle densities, eGFRD2 is up to 3 orders of magnitude faster
than optimized Brownian Dynamics. We exemplify the capabilities of eGFRD2 by
simulating an idealized model of Pom1 gradient formation, which involves 3D
diffusion, active transport on microtubules, and autophosphorylation on the
membrane, confirming recent results on this system and demonstrating that it
can efficiently operate under genuinely stochastic conditions.
