%********************************************************************************** % % CalC version 5.4.0, script "YamadaZucker.par" % Victor Matveev, January 4, 2005 % % This script reproduces Fig. 3b from the paper by M. Yamada and R. Zucker, % "Time course of transmitter release calculated from simulations of a calcium % diffusion model" (1992) Biophys J 61:671-682. %__________________________________________________________________________________ % %================================================================================== % 1. GEOMETRY DEFINITIONS %================================================================================== volume 0.0 0.965 0.0 0.965 0.0 2.0 % Next line defines the grid (discretization of space) for the numerical solver. % The number of points along each of the three directions is 30. This grid size % guarantees a numerical accuracy of about 5 % grid N N N N = 30 % To improve the spatial resolution, we use a non-uniform grid, with a higher % density of grid points close to the active zone (spatial gradients are the % largest in this region, so higher spatial resolution is required). The grid is % smoothly stretched in all directions away from the active zone; for a % given direction, each successive grid interval is given by a product of the % previous grid interval, and a factor slightly greater than one, defined by the % "stretch.factor" constant: stretch.factor = 1.05 % The following "stretch" commands describe the region of space where the grid % points are dense. The grid is stretched in all 3 directions away from this region. % In this case, the dense region is a 400 nm by 400 nm patch in the xy-plane, % containing the 16 Ca2+ channels (see "Ca.source" definitions above) stretch x 0.0 0.4 stretch y 0.0 0.4 stretch z 0.0 0.0 %================================================================================== % 2. CALCIUM PARAMETERS DEFINITIONS %================================================================================== Ca.D = 0.6 % The Ca2+ difussion coefficient (in units of um^2/ms) Ca.bgr = 0.0 % Background Ca2+ concentration = 0 sigma = 0.01 % half-width of the spatial channel current density (see "Ca.source" % definitions below; allowing a non-point current source increases % the spatial accuracy of the method Ca.source 0.05 0.05 0 sigma sigma sigma Ca.source 0.05 0.15 0 sigma sigma sigma Ca.source 0.05 0.25 0 sigma sigma sigma Ca.source 0.05 0.35 0 sigma sigma sigma Ca.source 0.15 0.05 0 sigma sigma sigma Ca.source 0.15 0.15 0 sigma sigma sigma Ca.source 0.15 0.25 0 sigma sigma sigma Ca.source 0.15 0.35 0 sigma sigma sigma Ca.source 0.25 0.05 0 sigma sigma sigma Ca.source 0.25 0.15 0 sigma sigma sigma Ca.source 0.25 0.25 0 sigma sigma sigma Ca.source 0.25 0.35 0 sigma sigma sigma Ca.source 0.35 0.05 0 sigma sigma sigma Ca.source 0.35 0.15 0 sigma sigma sigma Ca.source 0.35 0.25 0 sigma sigma sigma Ca.source 0.35 0.35 0 sigma sigma sigma Ca.bc Noflux Noflux Noflux Noflux Pump Pump bc.define Pump 1 -0.133 0 %================================================================================== % 3. BUFFER PARAMETERS DEFINITIONS %================================================================================== buffer Bf Bf.D =0.0 Bf.kplus =0.5 Bf.kminus =25.0 Bf.total =2000 %================================================================================== % 5. SIMULATION RUN PARAMETERS %================================================================================== Run adaptive 1.0 ; current I1 Run adaptive 0.4 ; current I2 Run adaptive 3.6 ; current 0.0 Run adaptive 1.0 ; current I1 Run adaptive 0.4 ; current I2 Run adaptive 3.6 ; current 0.0 I1 = 1.35 I2 = 4.6 %================================================================================== % 6. DATA OUTPUT %================================================================================== dCX/dt = 2 kx.off C2X + 4 kx.on C X - ( kx.off + 3 kx.on C ) CX dC2X/dt = 3 kx.off C3X + 3 kx.on C CX - ( 2 kx.off + 2 kx.on C ) C2X dC3X/dt = 4 kx.off C4X + 2 kx.on C C2X - ( 3 kx.off + kx.on C ) C3X dC4X/dt = kx.on C C3X - 4 kx.off C4X X := 1 - CX - C2X - C3X - C4X % Conservation constraint for the X-sensor CX(0) = 0 ; C2X(0) = 0 ; C3X(0) = 0 ; C4X(0) = 0 % Initial conditions C := Ca[0,0,0] % 2. Next, we define the equation for the facilitation Y-sensor: dCY/dt = ky.on C ( 1 - CY ) - ky.off CY CY(0) = 0 % 3. Finally, the equation for the release rate: dRelease/dt = k2 C4X CY - k3 Release Release(0) = 0 % 4. Now we define the rate constants in the above system of equations (Y.kon will be % redefined for the simulations with tortuosity, Figs. 2D and 3D; in that case the % Y-sensor affinity is changed to 9 uM) kx.off = 100 ; kx.on = 0.5 % For the X-sensor affinity = koff / kon = 200 uM ky.off = 0.15 ; ky.on = 0.01 % For the Y-sensor affinity = Y.koff / Y.kon = 3 uM k2 = 1 ; k3 = 1 % These define kinetics of the release rate variable %================================================================================== plot.print "yamada.zucker." plot C plot Release % plot.method xmgr %================================================================================== % T H E E N D %==================================================================================