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Manuscript Title: CA3D: a Monte Carlo code to simulate 3D buffered diffusion of ions in sub-membrane domains.
Authors: A. Gil, J. Segura
Program title: CA3D
Catalogue identifier: ADNW_v1_0
Distribution format: tar.gz
Journal reference: Comput. Phys. Commun. 136(2001)269
Programming language: Fortran.
Computer: SUN Enterprise 3000, PC Pentium III 450MHz, PC Pentium II 350MHz.
Operating system: Solaris (SunOS 5.6), GNU/Linux, Win32.
Supplementary material: Pseudocoloured animated images of calcium 2D maps obtained from the simulation.
Keywords: Biology, Ion diffusion, Random walk, Buffering, Reaction-diffusion.
Classification: 3.

Nature of problem:
The buffered diffusion of ions in the sub-membrane domain of cells is simulated by means of Monte Carlo methods. Two geometries of submembrane domains are considered. The first, a conical domain, applies to spherical cells with a locally uniform distribution of channels while the second, a cylindrical domain, is intended to model ciliar cells and presynaptic terminals. Other domains can be implemented in the code with ease. The entry of ions takes place through discrete entry points (channel pores) which are distributed over the compartments of the first slice of the domain (base of the cone or the cylinder). Ions diffuse inside the cell and react with endogenous or exogenous buffers, mobile or fixed.

Solution method:
The diffusion of ions and binding molecules is modeled as a 3D random walk process by moving each individual ion and molecule. The reaction of ions with the binding molecules is also modeled probabilistically.

The number of radial grid points is restricted to 100 (diameter 200 points). The depth is limited to 100 grid points. In case the grid resolution and the sizes of the domain are chosen is such a way that this limit is surpassed, a warning message is generated and the program gives the option of continuing the simulation by taking the largest possible sizes of the domain, maintaining the spatial resolution. The number of grid points available could be smaller in other (generally older) computer systems, depending on the RAM available. In all the systems checked (with a RAM of 64MB or higher) the restrictions on the number of grid points described above were always within computable ranges. The dimension of the arrays limit the resolution and size of the domain of simulation that can be taken into account. In this way, for domains with a typical size of L, the best resolution achievable is of the order of L/100.

Running time:
Depends on the buffers, grid resolution, unitary current, etc. For example, for a conical domain of 1 mum radius and 5 mum deep, a calcium time course lasting 1 ms takes 34 s of CPU time for a resolution of 100 nm and 378 s for a resolution of 50 nm; in both cases a standard endogenous buffering is considered with the addition of an exogenous buffer (Fura-2 100 muM). See section "CPU times" for more details.