Before revision:  MLM run time is an order of magnitude faster than eGFRD when diffusing macromolecules with typical concentrations reported in the cell.abstract 
After revision:  MLM run time is an order of magnitude faster than eGFRD when diffusing macromolecules with typical concentrations reported in the cell.abstract \% larger than the molecule. MLM is validated by numerical simulations, showing good agreement with the off-lattice particle-based method, eGFRD. MLM run time is more than an order of magnitude faster than eGFRD when diffusing macromolecules with typical concentrations in the cell. MLM also showed good agreements with eGFRD and mean-field models in case studies of two basic motifs of intracellular signaling, the protein production-degradation process and the dual phosphorylation cycle. Moreover, when a reaction compartment is populated with volume-excluding obstacles, MLM captures the non-classical reaction kinetics caused by anomalous diffusion of reacting molecules.