2013/04/27 by Mark B. Flegg, Flegg, Mark B, Stefan Hellander +3 · 1 citation
Biochemistry, Genetics and Molecular Biology · Computer Science · Mathematics · Physics and Astronomy · #Advanced Mathematical Modeling in Engineering #FOS: Biological sciences #Gene Regulatory Network Analysis #Mathematical Biology Tumor Growth #Subcellular Processes (q-bio.SC) #Theoretical and Computational Physics
paper · pdf · doi:10.48550/arxiv.1304.7393
openalex publication_date 2013/04/27 · openalex created_date 2022/10/06 · openalex updated_date 2026/07/28
In this paper, three multiscale methods for coupling of mesoscopic\n(compartment-based) and microscopic (molecular-based) stochastic\nreaction-diffusion simulations are investigated. Two of the three methods that\nwill be discussed in detail have been previously reported in the literature;\nthe two-regime method (TRM) and the compartment-placement method (CPM). The\nthird method that is introduced and analysed in this paper is the ghost cell\nmethod (GCM). Presented is a comparison of sources of error. The convergent\nproperties of this error are studied as the time step \Δ t (for updating\nthe molecular-based part of the model) approaches zero. It is found that the\nerror behaviour depends on another fundamental computational parameter h, the\ncompartment size in the mesoscopic part of the model. Two important limiting\ncases, which appear in applications, are considered: (i) \Δ t approaches 0\nand h is fixed; and (ii) \Δ t approaches 0 and h approaches 0 such that\n\Δ t/h2 is fixed. The error for previously developed approaches (the TRM\nand CPM) converges to zero only in the limiting case (ii), but not in case (i).\nIt is shown that the error of the GCM converges in the limiting case (i). Thus\nthe GCM is superior to previous coupling techniques if the mesoscopic\ndescription is much coarser than the microscopic part of the model.\n