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Microscopic models of reaction-diffusion processes on the cell membrane can link local spatiotemporal effects to macroscopic self-organized patterns often observed on the membrane. Simulation schemes based on the microscopic lattice method (MLM) can model these processes at the microscopic scale by tracking individual molecules, represented as hard spheres, on fine lattice voxels. Although MLM is simple to implement and is generally less computationally demanding than off-lattice approaches, its accuracy and consistency in modeling surface reactions have not been fully verified. Using the Spatiocyte scheme, we study the accuracy of MLM in diffusion-influenced surface reactions. We derive the lattice-based bimolecular association rates for two-dimensional (2D) surface-surface reaction and one-dimensional (1D) volume-surface adsorption according to the Smoluchowski-Collins-Kimball model and random walk theory. We match the time-dependent rates on lattice with off-lattice counterparts to obtain the correct expressions for MLM parameters in terms of physical constants. The expressions indicate that the voxel size needs to be at least 0.6% larger than the molecule to accurately simulate surface reactions on triangular lattice. On square lattice, the minimum voxel size should be even larger, at 5%. We also demonstrate the ability of MLM-based schemes such as Spatiocyte to simulate a reaction-diffusion model that involves all dimensions: three-dimensional (3D) diffusion in the cytoplasm, 2D diffusion on the cell membrane, and 1D cytoplasm-membrane adsorption. With the model, we examine the contribution of the 2D reaction pathway to the overall reaction rate at different reactant diffusivity, reactivity, and concentrations.

Lattice-based stochastic simulators are commonly used to study biological reaction-diffusion processes. Some of these schemes that are based on the reaction-diffusion master equation (RDME) can simulate for extended spatial and temporal scales but cannot directly account for the microscopic effects in the cell such as volume exclusion and diffusion-influenced reactions. Nonetheless, schemes based on the high-resolution microscopic lattice method (MLM) can directly simulate these effects by representing each finite-sized molecule explicitly as a random walker on fine lattice voxels. The theory and consistency of MLM in simulating diffusion-influenced reactions have not been clarified in detail. Here, we examine MLM in solving diffusion-influenced reactions in three-dimensional space by employing the spatiocyte simulation scheme. Applying the random walk theory, we construct the general theoretical framework underlying the method and obtain analytical expressions for the total rebinding probability and the effective reaction rate. By matching Collins-Kimball and lattice-based rate constants, we obtained the exact expressions to determine the reaction acceptance probability and voxel size. We found that the size of voxel should be about 2% larger than the molecule. The theoretical framework of MLM is validated by numerical simulations, showing good agreement with the off-lattice particle-based method, enhanced Green's function reaction dynamics (egfrd). MLM run time is more than an order of magnitude faster than egfrd when diffusing macromolecules with typical concentrations observed 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-dephosphorylation cycle. In addition, when a reaction compartment is populated with volume-excluding obstacles, MLM captures the nonclassical reaction kinetics caused by anomalou

This paper describes the effect of friction pressure on the joining phenomena of friction welds between pure titanium (P-Ti) and pure copper (OFC). When the joint was made at a friction pressure of 60 MPa or lower, the OFC side had deformation from the contact of both weld faying surfaces. Then the joint had generated sparkle from the P-Ti side with increased friction time. The peripheral portion of the P-Ti side had large deformation and was intensely upset when the joint had sparkle. On the other hand, the joint did not have sparkle on the P-Ti side when it was made at a friction pressure of 75 MPa or higher. The deformation of the OFC side was large and was intensely upset, although the P-Ti side was hardly deformed. The joining phenomena had dissimilarity because the difference of the yield stress for each material depended on the temperature in the friction process

This paper describes the effect of post-weld heat treatment (PWHT) on joint properties of copper?zinc alloy (brass) and low carbon steel friction welded joints. The as-welded joint obtained 100% joint efficiency and the brass base metal fracture without cracking at the weld interface, and had no intermetallic compound layer. The joint efficiency with PWHT decreased with increasing heating temperature and its holding time, and its scatter increased with those increasing parameters. When the joint was heat treated at 823 K for 360 ks, it did not achieve 100% joint efficiency and fractured between the weld interface and the brass base metal although it had no intermetallic compound. The cracking at the peripheral portion of the weld interface was generated through PWHT. The cracking was due to the dezincification and the embrittlement of the brass side during PWHT.